Fifteen minutes is pretty common especially for smaller stations. I have had five minutes where I got off the train, stood there, train leaves, wait five minutes, new train arrives, and I get on. However, you should not be slow about getting off. Most experienced riders will gather by the door, luggage in hand, a couple minutes prior to the train arrival. It is a bit of push as everyone jams to get off.
If you miss a train because it is late, what you do next depends on the type of ticket you hold. If traveling on a Regionale train ticket, then you just get on the next Regionale train. Any other ticket will need to be exchanged for a new ticket with a new seat reservation. Do not attempt to jump on the next without the proper seat reservation -- if caught, the fine is substantial and immediate. Take you old ticket and go to the ticket window for a new ticket. The ticket window will know that the train was late and it was not your fault for missing the connection.