Warning: spoilers ahead for anyone not having finished the game!
In the first cutscene of the game, we see a specific illithid infect the protagonist, as well as Lae'zel, with a tadpole. Other illithids lay on the floor, dead or unconscious, which implies these illithids were attacked by the one that infected us.
Later we find out that this illithid is the one that is using the Astral Prism to protect us from the influence of the Absolute. It's not said out loud (that I saw), but based on the clothing and look of it, this is clearly the same character.
So… why? Why did The Emperor infect Tav? Weren't we going to be infected and released anyway? Many other had been. Was there something about us that made us interesting to The Emperor? Were the tadpoles used on us different from those used on everyone else?
It seems like leaving the Prism with us was all that was needed. And even that could have been done after we left the ship.
Best Answer
While to my knowledge, it isn't perfectly spelled out in-game, a reasonable hypothesis follows (basically this whole Answer is major spoilers):
The Chosen of the Dead Three come up with a scheme to steal an ancient Netherese artifact (The Crown of Krasus) and use it to dominate an Elder Brain (aka, the Netherbrain) to do their bidding. They do so. The Nether Brain does not like being magically enslaved, and begins to plot an escape.
The Emperor was a mindflayer operating outside the purview of an Elder Brain (and, in fact, had spent literal years waiting for an opportunity to escape). When its organization ran up against Gortash's influence in Baldur's gate, its true nature is discerned and, thus revealed, Gortash and co. bring The Emperor under the Netherbrain's thrall.
The Netherbrain, after dominating The Emperor, realizes two things: First, The Emperor will go to great lengths to avoid being dominated and enthralled. Second, this is an opportunity, as it has already realized that if one of the netherstone wielders is slain, that will weaken its slavers' control and eventually allow it to escape the domination.
This allows The Netherbrain to conclude that The Emperor is likely to facilitate such a killing, in order to secure its own freedom (or, potentially, claim the Crown of Krasus for itself). One problem: The Chosen dominate the Netherbrain, and the Netherbrain dominates The Emperor. If the Chosen forbid it from acting against them, The Netherbrain's thralls are transitively bound to the same rules.
So The Netherbrain lets slip that the Astral Prism contains a power that allows one to resist the domination of an Elder Brain, and subtly insinuates that The Emperor would be the agent best suited towards retrieving it. The Chosen fall for the gambit, and The Emperor successfully acquires the Astral Prism.
This temporarily returns The Emperor to independence, but The Emperor is desperate for a more permanent solution. But The Emperor is but one monster -- they're still surrounded by Absolutist forces, and, it needs to hold onto the Astral Prism (made more difficult by the Orpheus' honorguard). In short, it needs help.
Remember - Illithids are intrinsically manipulative. [Cite: in game texts]. The best way it knows to "acquire help" is actually spelled "coerce".
So The Emperor makes its way to the recently captured and tadpoles as many as it can (remember, at this point all the other Mindflayers on the Nautiloid are still under The Netherbrain's control -- hence the illithid corpses in the opening cinematic).
Now that they have a "sword of Damocles" above their heads, all that's left to do is escape from the Nautiloid and begin puppeteering its new "allies". Since Gortash directed The Emperor to pilot the Nautiloid (as per his journals), this is actually quite easy -- allow the gith to catch up and down the ship, use its psionics to protect its newly tadpoled "friends" during the crash, and retreat into the Prism where it can suckle Orpheus' power to maintain the status quo.
So why Tav specifically? Convenience, really. Wrong place / wrong time. The Emperor needed someone who could fight against The Chosen and be manipulated into pursuing those goals. Tadpoling the cast allowed it to achieve both those ends.
One thing that doesn't fit nicely into the above understanding is how the Sharran artifact retrieval squad fits into things. Shadowheart claims that they steal the artifact from the gith, Gortash tasks the Emperor to do likewise, and both can't be true. Then again, Shadowheart's memories are all over the place, and a little memory manipulation seems perfectly within The Emperor's wheelhouse.
The other strange wrinkle is that if you are playing The Dark Urge, the opening cinematic scene isn't canon for you. Specifically, TDU is tadpoled before boarding the nautiloid.
Which leads to an open question: Perhaps the opening cinematic has been mildly retconned? The Emperor's eye color is wrong, for one, even if the cowl otherwise identifies it. Consider too, that the cinematic predates the game's final release by ~3 years, and that a full 3d cinematic like this isn't nearly as easy to change as writing or dialogue.
So in short: the cinematic isn't perfectly aligned with the implication, so it's also entirely possible that the premise of this question is false, and The Emperor is not the one who does Tav dirty. It's ambiguous, and there's yet to be anything to conclusively verify it, one way or the other.