Well, social skills are usually based on charisma.
Could we say for example:
- use powers to operate illithid device = int
- use power to gain understanding of something or learn the intentions of someone = wis
- use powers to manipulate the behaviour of someone = cha
- causing a physical effect is based on a physical stat and so on
So the tadpole gives you powers.
But you chose to use these powers (or not using them) with your own body and mind.
So the stat used depends on the exact effect you want to achieve with those powers.

Prof. Dr. Dr. Mad S. Tist

World leading expert of artificial stupidity.
Because there are too many people who work on artificial intelligence already