Season 1 episode 3 tickets

I am rewatching it and I am confused by the ticket checks. This may be due to my lack of knowledge of how trains work, but did either train employee actually check Don’s ticket in either train journey in the episode? In the second one, the employee hands him a paper, clicks a stamp in a ticket, then puts it in the pocket behind his head. Does this ticket belong to Don or the person sitting behind him?