From what I can gander they've been handed a 'fixed penalty notice'? But this issued only after someone's details have been taken by an RPI. I am therefore assuming the OP was not issued with any fine at the station. An RPI took their details and the OP was told they would get a letter explaining the course of action.
A fixed penalty notice, in Northern terms, is something that is issued on a discretionary basis after a person has been reported for potential prosecution. The OP did subsequently receive a letter.
At the same time, he was asked to purchase a ticket to cover the journey he made from Kirkham & Wesham and was going to make onto Manchester.
All we know is that the OP was advised to buy a ticket in order to continue their journey. It is not clear that the RPI advised purchasing a ticket from Kirkham. In any event, the offence is complete regardless of buying a ticket for the journey after the even.
Although it is very common for fines or court summons to be issued close to the 6 month limitation period (6 months after the incident occurred) as this is the cut-off point for taking any suspected fare evader to magistrates.
The 6 month limit is for the case to be laid before the court, not for the summons to be issued or for the case to be heard.
And yes I always advise people to be wary about what they say to RPIs. Even "no comment" or a shrug of the shoulder would suffice in many cases.
I find that saying "Good morning/afternoon/evening" and presenting a valid ticket suffices in every case. Being uncooperative is rarely a good idea, and I would suggest that the same applies to listening to your advice.