I don't think Putin pays him, at least not directly. There's plenty of leverage on him through his loans from Russian banks, which of course do business at the pleasure of Putin and were thus inclined to make "suggestions" about hires.
I'm sure the Kremlin did donate to the campaign, just like it does with a lot of right-wing populist campaigns in the West. Win or lose, they do a lot to destabilise democratic institutions.
That the GOP leadership joke about party officials taking Putin's ruble is repulsive but not surprising.
[* perhaps Rohrabacher is in thrall to Putin for similar reasons, or maybe there's some pee-pee-style kompromat]