So, does each mask have a specific magic assigned to it or does the magic manifest based on whoever wearing it? Like was Marvin's already an Illusions mask or did it give him illusion magic after the fact?
the magic manifests to the person, not to the mask. The mask is just a control device for the puppeteers. It depends on the person when they get masked if they get powers or not and which kind of powers they get. It often depends on personality and mental state before masking.
However, there is a link after the mask is equipped and the person's magic has manifested.
If the person's mask is removed, like in Henrik's case, they will retain their magic to a smaller degree, unless one of two things happens:
1) they get their mask back, in which case that control allows their magic to come back fully or
2) the mask is destroyed, and the magic is lost.
In Jackie's case, his mask was broken/melted into his face, which only strengthened his bond with the magic, making him stronger and harder to control.
[ We can still control him but it is more difficult for me, so Anti usually takes direct control of him. He gets special treatment :) ]