If I use Feraligatr's "Torrential Heart" Ability and then use Prime Catcher to bring my opponent's Flutter Mane into the Active Spot, would my Feraligatr's attack damage still be boosted?
Yes, even though Flutter Mane is disabling Feraligatr's Ability the Torrential Heart effect was already applied until the end of the turn.
Source: Temporal Forces FAQ; TPCi Rules Team (2024-03-21)

Relevant cards

Note: All applicable cards may not be listed below.
SV5_41
SV5_41
SV5_78
SV5_78
SV5_157
SV5_157