The last ability of Norn's Inquisitor will trigger if a permanent you control transforms in either direction, going from front face up to back face up or vice versa, as long as it's a Phyrexian after doing so.

Only transforming double-faced permanents (including transforming double-faced cards and Incubator tokens) can transform. A face-up permanent turning face down doesn't count as transforming, nor does a face-down permanent turning face up.