Killing Bob in a cut-away scene isn't announcing trouble elsewhere. Doing that violates an important Keeper Principle: Address yourself to the characters, not the players. A move must always follow the Principles, so announcing can't be used to reveal something "off screen" that way.
Announcing trouble elsewhere is smoke on the horizon, figuratively (and sometimes literally): it's an event or detail that the characters witness, that makes the players wonder what's going on and whether they should run and hide, or investigate. This is an example of announcing trouble elsewhere that could follow a puzzle things out player move miss:
Player: I found this thing, what does it mean? rolls a 6
Keeper: You collect yourself and ponder it, but your thoughts are interrupted as a misshapen shadow suddenly falls across the drapes in the window across the room. A heartbeat later it's gone. At the same moment there is a frightful banging on the front door, and you hear Bob shouting: "Open the door! For the love of God, open up!"
Keeper: What do you do?
Foreshadowing is similar, but subtler. A wind rises ominously outside the house, blowing so strongly that it howls "like a wolf". It really is just the wind, but that's foreshadowing in a story about werewolves. You don't have to (and actually shouldn't) let your players know that what you just said is only foreshadowing. Let them figure it out. Let it scare them.
Remember another Principle: Make your move, but never speak its name. Just because you are making a foreshadow or announce trouble move doesn't mean you have to tell or show the players what the trouble is. They don't have to know that you're making a trouble-related move at all. All you have to do is foreshadow something or announce something: the player's job is to respond to what you've just made happen and figure out what it means. If you show them that what you're doing is foreshadowing or announcing trouble, then you might as well speak the move's name. Don't do that. Besides, it's not "foreshadowing" if you make it obvious what casts the figurative shadow.
tremulus is actually a fairly straight port of Apocalypse World. The player moves are not much changed, and the Keeper moves are almost identical. In particular, puzzle things out is a port of read a sitch, and can be responded to with MC/Keeper moves nearly identically.
Some ways to use the other Keeper moves for a miss on an attempt to puzzle things out:
Separate them
"You ponder the clue. Suddenly you realise you're alone, your companions no longer with you. What do you do?"
(Why are they separated? You don't have to know. Play to find out, just like the players.)
Capture someone
"You ponder the clue. A burlap sack drops over your head as your feet are swept out from under you. You land with a thud that knocks the wind out of you, and a moment later you feel soft hands binding your hands with rough rope. What do you do?
Put someone in harm's way
"You ponder the clue. Looking up briefly, you see the glint of gun's barrel poking through the ajar door, pointed at [insert someone, maybe the PC, here]. What do you do?"
Take away their stuff
"You sit in the train station, leafing through the odd book you found. When you get up to go, you see you bag is no longer at your feet. A sudden pelting of feet, and you look up just in time to see the thief disappear through the door to the platform, glancing over their shoulder at you."
or
"You examine the clue by the light of your candle, but a sudden gust of wind blows it out. You're out of matches, and you're in the dark in a strange house. What do you do?"
Make them buy
"You ponder the book, but you can't make heads or tails of it. It looks similar to something you once saw in mad old Alaric's sitting room though, so perhaps he can make something of it. Though of course, he never lets in visitors who don't bring a gift, and his tastes run to the pricey and exotic. What do you do?"
or
"The book is written in Cyrillic, of all things. You're going to need to contract with a professional translator."
Activate their gear's downsides
"You ponder the clue as you walk down the street, but your unwieldy luggage keeps tripping you up and you get no good thinking done. You realise that you're not going to make the 4:16 train at this rate. What do you do?"
Tell them the possible consequences and ask
"The book looks to be full of strange diagrams and spidery handwriting that is more erratic in later pages. Your guts twist as you merely glance at some of the drawings and your mind shies away like a skittish horse. Are you sure you want to study the book closely?"
(The consequence is risking madness, of course.)
or
"You can stop to read the book now, but if you do you'll miss the train the cultists had tickets for. What do you do?"
Offer an opportunity…
…with a cost
"You leaf through the book, skimming but not reading deeply. You realise that the book describes the ritual you aim to prevent, and should reveal when and where the cultists must hold it! Do you dare risk madness by studying it?"
(But that sounds like a successful roll! Yeah, well, that's how the game works. On an actual success, this wouldn't be a madness-inducing book. It's a shrödinger's book that way: on a miss it has complications that on a hit it wouldn't have. Remember, you don't know any thing for sure until it happens in play, and any of your prep details can be changed before they are introduced into play.)
…without a cost
"As you ponder the book, you realise that you're getting nowhere. You look up from it, and realise that as you read your taxi driver brought you mistakenly to a part of town you've never visited. And lo, on the door of a shop across the street is painted an innocent-looking company logo that cleverly incorporates a sigil that you know: the sign of the Cloistered Wardens, whose counsel in these matters is always valuable. What do you do?"
Turn their move back on them
Player: "I found this thing, what does it mean?" rolls a 6
Keeper: "I don't know, what do you think it means?"
or
"You sit in the darkened study, inspecting the book. As you leaf through it, a creeping horror dawns on you. You realise with rising revulsion and terror that, somehow, the book is reading you, malevolence radiating from its pages. What do you do?"'
Let the dice decide isn't often going to be applicable to puzzle things out. Usually, attempts to puzzle trivial things out won't result in a roll, you'll just tell them. "Does the paper have an obituary for the guy who died two days ago? I'm using puzzle things out…" picks up dice "Hey, put the dice down. You didn't trigger a move. Yeah, he's in the obits."
Make a hazard move
While the character is inattentive, pondering the clue, a hazard makes a move. Pick one. The storm gets worse, the graves nearby open up as the dead rise, the phone rings and it's that meddling police officer requesting that you come down to the station for another chat. The phone rings and it's a hollow voice that speaks in tongues you've never heard. The book flips shut, as if of its own accord. The scratching behind the walls starts up again.
Inflict damage
If the PC is stopping to puzzle while in danger (perhaps whether they know it or not), hurt them. Bam.
Present items and clues
"As you ponder the book, an envelope falls out. Someone must have tucked it into the pages. What do you do?"
Reveal knowledge
"As you ponder the book, you realise it's made of human skin. What do you do?"
(This is your opportunity to reveal whatever you want, not necessarily what the player was hoping to learn about.)
A few other quibbles with some things you wrote:
"…they roll poorly, something bad happens to them in the process."
No. A Keeper move is not a bad thing, necessarily. A move is merely something that happens next. Consider the move Offer an opportunity, with or without a cost. If you choose to offer it without a cost, an opportunity is the opposite of a bad thing. All moves are like this: they are things that happen. Whether they are bad or not is a matter of context. Don't try to make bad things happen, just make things happen at all that fit the moves. (The badness will take care of itself.)
Dungeon World's reveal an unwelcome truth is actually a limited subset of announce trouble elsewhere. Announce is actually more flexible, not less: making an announce move can be revealing an unwelcome truth, and it can also be saying that the PCs hear the clangor of a fire engine speeding toward them.
