You can do that attack with the townies fighting style pressing R (grab) but jimmy doesn't have that stance.
Is that the fighting style from the guys from happy volts?
Only with the grapplers, that is.
And yes. He uses the Bully's punches with this particular style. But it's unique in that the second punch doesn't actually do damage, whereas the first punch deals quite a bit of damage, and the third punch does slightly less.