Placing time limits on turns further couples character skill and player skill. This is not a bad thing inherently, but it is a bad thing in many playstyles. You need to make sure you and your players are on the same page before doing that. You can allow character differences to play in somewhat, for example, I once played a round of D&D 3.5 (which is basically Pathfinder) with a sort of speed-chess like system for out of game turn time limits. The base time per round was intelligence based while the maximum you could have banked at once was wisdom based. Nonetheless, this system will always add a significant element of player skill to the game that wasn't there before, and people may be upset about that.
There are no other drawbacks, but the tie-in to player skill has a number of complications. The most fundamental one is that it changes what sorts of characters players can make. While it does let players who are fast on their feet make and play characters that would otherwise be impossible to pull off, this will not be noticed as much as that all players, but especially slower ones, will not be able to play characters that they otherwise would be able to play.
That said, there are a LOT of drawbacks to your specific implementation:
1) The implementation is non-symmetric. The GM has no limit on their turn, which basically nullifies most of the benefits of timed turns in the first place. Furthermore, it is rather condescending.
2) Players can't collaborate during combat because they can't talk to each other without waiting a round this is kinda ridiculous and will break the kind of simulationism you claim to be seeking.
3) Your rules cause a lot of problems with the pathfinder rules. Specifically, there are many, many actions that can be taken out of turn. Your rules don't allow for that, so, for example, if I use an immediate action at the start of another player's turn, I will have the opportunity to fully negate their turn. Furthermore, I have no time limit applied to me at such a time. I can declare that I'm casting featherfall as an immediate action, and dither over the target indefinitely. Everybody loses their actions, but it's not like the bad guys can do anything until I pick who I'm targeting because the immediate action has no time limit. In fact, if I'm not engaging in PvP, such abilities are probably unintendedly powerful in your system, since engaging them during an opponent's turn allows all the players time to think. Of course, declaring the action will be difficult since you can't talk even OoC out of turn, but you presumably could say during your turn "I cast featherfall during the turn of the first goblin that gets a turn before it can do anything".
3b) Readied actions pose a similar problem: "I ready to strike the dragon when it swoops by me" Later.. "Ok, the dragon swoops by you, do you attack it?" "...". Having to declare whether to use the readied action or abandon it during your own turn is very problematic.
3c) players with lots of characters are much advantaged by this system. In fact, having bag of enslaved rats is basically necessary for party communication. Since player communication is tied to character turns, having a bunch of alternating rat turns with rats completely irrelevant to the combat allows players to talk to eachother out of character and to request clarification from the GM.
3d) this system encourages players to shout over eachother. If I'm engaging in PvP with another player, I should try to interrupt their turn with as many actions as possible in order to divert GM focus and cause them to lose their actions. In order to prevent this, I should ignore and talk over the GM during my turn so that my actions have been stated within the time limit. This will make the already strained relationship this system lends itself to worse.
4) loss of action is too severe a penalty. The drawback to an overly severe penalty is that life and death will often be a matter of accident. This is worse in that the system is horribly one-sided. The default action system mitigates this, but not well (see #10)
4b) Furthermore, this penalty makes no sense in the fiction, while you are seeking fictional realism. This is bad.
5) The absurd and overly harsh limits on player participation, especially player verbal participation, limit player agency in the sense players normally participate in Pathfinder.
6) The absurd and overly harsh limits on player participation, especially player verbal participation, set the players against the GM. This game will be a game about rebellion and defiance, not in the game-fictional sense, per se, but in a postmodernist sense. The players, to exercise agency, must trick you, find loopholes in your regulations, and engage in positive collaborative experience despite your attempts to crush their spirits, forbid them from exercising any creative or perceptive inclinations, and generally stop them from having fun.
7) This system will make combats drag on a very, very long time-- in fact I rather suspect they would never end at a certain point-- and abstract the focus of the game to how the players can exclude the GM rather than anything interacting with the game world. This does not sound like something I would have fun GMing, and it also runs contrary to your stated objectives.
8) A lack of time limit on math allows players to use math to get more time. Cast a spell requiring the GM to solve a partial differential equation before casting one that you need time to figure out. Again, talk over the GM while he's trying to do the maths so that way you can get extra info on the record and give your teammates more time to think and more info about what you're doing.
9) This dramatically increases GM bookkeeping and the reliance on GM discretion since the new rules are largely hand-wavey in terms of what counts as what and the GM will need to constantly arbitrate these new rules.
10) The default action system bypasses most of these problems. Players should lay out a complicated and elaborate interlocking network of conditional statements that form a comprehensive party plan as their default action. Then the players should go off and do something fun while the GM resolves combat, as they wouldn't be able to participate much, anyways. This excludes the GM from the fun group activity that the players get to do while he or she runs the combat out mechanically according to the players' default action flow chart. It also means that the players' will not be very engaged with the combats and will need to be brought up to speed as to what happened afterwards. The GM will also probably be told they misapplied certain sections of the flow chart at least sometimes, and thus end up going back and recalculating things again.
Basically, timed systems only have the inherent difference that they included 'using timed systems' as a part of the skillset game performance is based off of. Your timed system, however, is very, very problematic and would best be avoided. If your goal is to achieve a more intense combat with more engaged players, I suggest you ask about how to do that in a separate question, or even how to do that with time-management.
Extra information regarding speed-chess as a timing system:
I really like the speed chess version of this and if you choose to do it, I'd recommend you go that route. You can get apps for that for smartphones and computers and stuff, and it allows for a very flawless switch between timers. So, like, GM sends it to Bob's turn for combat and Bob asks for a description of the orcs and hits it back to the GM who hits it back when he's done describing.
You can learn more about the different kinds of speed chess [here](
en.wikipedia.org/wiki/Chess_clock#Time_controls). We used something based off of the Fischer system with Int score/2 seconds as the per-turn delay, Wis score/2 minutes as the starting and maximum banked times each combat, and Con score/2 seconds as how much time you get back every time you fully run out of time at the cost of increasing penalties. If I remember correctly the penalties were something like fatigued-->exhausted-->unconcious, except I think being staggered played in somehow. In any case, I don't remember the rules entirely and I don't have them any longer so you'll have to come up with your own adaptation.
If you decide to use sandglasses, you will want a lot of extras so no one has to sit around awkwardly waiting for the sand to run out after someone took a fast turn. Generally, sandglasses should be avoided, though.
If you use some variety of digital timer, that would be better than sandglasses but dedicated timing software more directly designed for your purposes will work even better. At the very least, you need to be able to reset the timer to a preprogrammed value with ease (at least, if your GM timing limitations for NPCs ends up working anything like ours did. You could also base something off of that many-v.s.-one grandmaster exhibition format, but I don't know if they make timers that have a pool for that sort of game that could work for this. There is a chess stack exchange, you could ask there. Actually, that sounds like a useful thing just for playing chess as well so I asked about it. You can see the question here.