You are wrongly assuming that what is printed on the ticket is a schedule. It is not. Tickets are for a route, not a train. You have a ticket Basel to Chiasso, and another Chiasso to Milano and then on to Rome. That has to do with the different ways the tariff system works in Switzerland and Italy.
In Switzerland you always have one single ticket from origin to destination, irrespective of how many trains, trams, busses ore other means of transport are involved.
In Italy you have a separate tickets for regional and long distance trains. Long distance train tickets have a reservation included in Italy.
In order to accommodate that the system split the booking for you at the border wich is Chiasso. So what you have is:
A ticket Basel - Chiasso. This ticket is good for all trains on that route, within the time of validity printed on that ticket. This is a ticket according to the Swiss Tariff, good for a route.
A ticket Chiasso - Milano. This itcket is again good for all trains on that route, within the time of validity printed on it. So those places, times and dates are not a train schedule, they just indicated where and when your ticket is valid. This will be a ticket according to Italian regional tariff, again good for a route.
A ticket Milano - Rome. This is a combined ticket + reservation for a Milano - Rome service. This ticket is just good for that train. But if you have a delay and that makes you miss the connection you can just have that ticket exchanged at the info desk at the head of the platforms in Milan.
So you are all set. Just follow the schedule in your travel docs, and show your tickets on board the train when requested.
Note: When is this trip? This is an odd routing. There are normally direct trains from Basel to Milano, and the obvious choice would have been one of those.