I don't think he's upset about the fines being paid, per se.
The cynic in me can't help but think that he (and his caucus) are upset about having to pay the fines themselves via payroll deduction (as opposed to some union cutting them a check and paying them that way, or them paying the fines out of their campaign committees or whatever else they might cook up to avoid the money coming out of their own wallets).
Bauer met with GOP leaders for hours because they are upset about fines and procedures related to the five week walkout that ended Monday. Bauer says they will pay the fines but don’t the fact that they are being deducted from paychecks.
Basically, they were willing to pay the fines so long as they could find a way to get someone else to pay it for them. Now that they have to spend their own money, they're upset. Sounds like a Democrat to me.