About the timing
First, five rounds is much, much too long. A typical combat is decided in 2-3 rounds; a 5-round combat is really long. Maybe with a lot of mooks to mop up things could drag on that long, particularly if their appearance is staggered so they can’t all be caught in one area blast, but that doesn’t generally make for a very good fight.
In fact, so much happens in a single turn, to say nothing of an entire round, that giving the players even a full round of combat before the monsters become “real” is quite a substantial advantage for them. I would go with just one round.
About the balancing
Second, this kind of thing isn’t really a matter of rules. I mean, I suppose they could have written up something for this, but I’m pretty sure they haven’t—it’d be pretty surprising if they had. You’re going to have to just do it as a matter of DM fiat. Which is fine, it just means a little more work on your part getting the numbers right.
Specifically, if you have a bunch of Tiny monstrous spiders at CR ¼, but after one round they balloon into Small monstrous spiders at CR ½, whether you should be counting them as CR ¼ or CR ½ depends a lot on how many there are, and how many the party can eliminate in one round. If the party can and will blast them all immediately—whether that’s an archer with a ton of arrows per round, a warrior with Whirlwind Attack or something similar, or a mage with burning hands or fireball or whatever and willing to use it, most of them are going to be gone before they actually become CR ½. Even if not, you figure they party is probably going to go through roughly one each, so if you only have 4, once again, all gone. If you have 20, and they only go through 4, they have 16 left that are now Small—each CR ½—and maybe your encounter is looking more like it’s at that CR.
If you plan on having them grow again in round three, I’d just ignore that. Some might still linger by that point, but if the party has their act together it shouldn’t be many.
So anyway, you basically have to imagine how the players are going to react, and scale it accordingly. You have to think about what their capabilities are, and whether or not they’re likely to respond to this threat quickly. If their area-damage options are limited, maybe they won’t use them on Tiny spiders—maybe it’s OK if they trivialize the encounter by spending a spell slot or whatever. If their area damage options aren’t limited, and you assume they’ll use them, then maybe you want the encounter to be bigger to make up for that. Or maybe you want to leave some people still OK, so they can’t just blast all the spiders. Up to you, really, but the more complicating factors you throw in—the less likely they are to be able to mop up the spiders in a timely fashion—the more this is looking like the higher CR option than the lower.
Also, for the record, I chose the Tiny and Small spiders because you mentioned Tiny in your question. Scaling this up—having the spiders start Medium and become Large, for example—should work out OK enough, up to a limit anyway. But then the spiders are presumably limited to being smaller than their hosts, so it may not matter., that’s really not so different from any other case—CRs and player character power levels are both so wildly variant that CR is terribly unreliable. No matter what you do, you have to carefully consider how your party is going to deal with this encounter if you really want to know how it’s going to go.
About how this compares to the rest of the game
Third, that’s really not so different from any other case—CRs and player character power levels are both so wildly variant that CR is terribly unreliable. No matter what you do, you have to carefully consider how your party is going to deal with this encounter if you really want to know how it’s going to go.