What I can tell for sure is that using the tadpole against Lae'zel after talking to Zorru does not use up your daily ilithid power and does not trigger a dream. At least not for me as of patch 3. Using the tadpole against Wyll when talking to him about his sending stone also does not trigger a dream for me, but it does use up the daily ilithid power. This has been happening to me in all post patch 3 playthroughs (I've done four so far).
Ah, understood. I have never used tadpole on Lae'zel, so unsure on that front.