I recently discovered this issue where punishes aren't boosted by rate of fire bonuses from pilots. Even when the Purple outline/visual appears on the punishers when getting the RoF bonuses, it still doesn't shoot any faster
For testing, the first clip is with Kate, who doesn't possess any RoF buffs. And the second clip is with Bullwork Liu, who has 2 perks that give an 11% RoF bonus combined.
P.S. the .02 second discrepancy isnt the buff coming into play, I believe a few shots from the punisher didn't hit/damage drop-off occured, resulting in a longer TTK in the first clip.