Screenshots or a better description might help.
First of all: there's a difference between fines and bounties. Which one are we talking about?
Second: IFs are only on low security systems and Anarchies. The latter are pretty rare. And especially if you're flying a large ship, you'll have to look around a bit (or check in Inara or EDDB)
Third: just because the System is controlled by the faction doesn't mean the station you docked at is controlled by them. You should see (at least for bounties, not sure about fines) your access set to "limited access", which means youcan pretty much only access the official station representative to pay your dues. Read the small print - if you have bounties and pay them off at the station, you'll end up in prison.
Oh - and if you gained these fines(?) in Oddity on foot, the above doesn't work. Just don't ask me what does work...