This version of the Professor lives in a domain called Paradox Castle, which is presumably the Professor's childhood home. 

Guarding paintings of their other selves, they are aware of how their other versions interact across the universe and ensures they are all kept in equilibrium.

When they meet Lily and Violet, the Professor testifies that they are trapped within the confines of the Castle, but sooner or later they find out this version is not telling them everything. . . .