"I would like to know how long they are going to keep the fine in their records"
They key word here is 'they'. Think who you mean by 'they', and it may answer your own question.
If you were 'fined' for bringing a Dutch library book back late, would the 'fine' be on Police records and accessed by immigration officers?
Were you fined' by police on the train? Or by NS Dutch railways? Are NS the police?
