She comes out from the chair.
If you look closely, she can easily fit inside the part where the cushion is suppose to be at but the back rest of the chair is a trap door for her to escape.
She has her legs tucked in and throws them outwards and closes the trap door and sets in to position before the illusionist removes the cover.
The whole backrest of the chair is flexible, the assistant or whoever it is is keeping it from going too much forward and unfolding which seems to be a part of this whole trick.