I think you are confused by the assumption that tomber is always intransitive.
In colloquial French, you can use it as a transitive verb with 2 meanings:
1) to take off a piece of clothing. It is frequent in the phrase tomber la veste, which you would say in situation where you are formally dressed with a suit, and you decide to relax a bit and take off your jacket (ex: on est entre nous, tu peux tomber la veste). Or a famous French song from the 90s had this line in its chorus: On va la tomber, tomber la chemise.
2) to seduce a man/woman. Ex: votre fils est très beau, il doit sûrement tomber toutes les filles
In the set phrases tomber le masque or faire tomber le masque à quelqu'un, it would be tomber used transitively as in the 1st meaning above, ie faire tomber le masque à quelqu'un will mean "to force someone to remove one's mask".
Note, however, that you will also find this expression where "les masques" would indeed be the subject of "tomber", used then intransitively. Grâce à cette discussion, les masques sont tombés.