Carlisle don't do any on train ticket inspections (or at least they shouldn't be). All on board inspections are done by Northern employed staff be that guards or RPIs. Carlisle do have PACE trained penalty fares collectors who work at stations and also staff the barriers at Northern stations (except Manchester Oxford Rd, Blackpool N, Liverpool L St, Leeds and Bradford Int where they are directly employed).
RPIs (both Carlisle Security and employees of Northern) can issue penalty fares both of which are subject to an appeals procedure. They can also fill in TIRs which may result in the prosecutions department offering an out of court settlement which some people see as a fine but these are not issued by the RPI.
As with all TOCs there will be a percentage of penalty fares given that will be appealed successfully, many will be given based on the evidence the issuer has at the time of issue, and new evidence may come to light on appeal.
You say there are some who just come along to fine people for minor errors? Can you give any examples? Minor errors that frequently occur on this forum include buying a ticket from the closest station to a barriered station, forgetting you actually got in several stops before. An RPI can only deal with what's in front of them, its a lot easier job if everyone presents a valid ticket.
I'm pretty sure I've seen them on trains doing inspections, perhaps this was during distruption.
I am aware they mostly work at stations, but it is genuinely useful to clarify where and when they work, thank you, because I wasn't aware of their barrier work (also interesting from an IR point of view - don't worry I'm not a union rep or anything though).
I would have thought they be directly employed, but a lot of the world of NT confuses me, to be fair.
I wasn't suggesting that people who deliberately evade fares don't deserve prosecution or PFs, it was more a comment about fining people due to Advance ticketing errors when Northern changes the timetable so frequently at short notice. If I'm honest, the whole principle of short to medium distance Advances in insane, especially on an operator as unreliable as Northern - people can't plan effectively for connections when you cannot rely on a train being on time and the frequency of service on some routes means it it easy to make mistakes confusing different services (sorry to those many guards, drivers and other staff who work for NT who put everything in day in and day out, but it's not up to scratch, mostly due to DfT meddling).