When does the pushing damage for theme prob take place?

The scenario in mind is blue recruit pushes to theme prob an ally, does the damage happen right away so he can use the prob he gets on his second click if the attack misses again, or does he take pushing damage after the ally is done with their action?

Thanks!

"After actions resolve" is the correct term I believe.

You believe correctly. Pushing damage happens after actions resolve.

On a side note, TTPC is still a use of PC so the Blue Recruit would not be able to Theme-Prob and then "regular Prob" later in the same turn.

It's actually "as actions resolve".

2014 rulebook page 8:

When a character receives a second action token
(usually because it has taken an action on two
consecutive turns), deal one pushing damage to
that character as actions resolve.

And yeah, it makes a difference, but the difference doesn't usually matter.