Tickets are for a route, not a train. You do not have train tickets. There is no such thing as a train ticket…
You have a ticket for the route Basel-Chiasso, and a separate one for the route Chiasso-Milano. This is done like this because the tariff systems are different between Switzerland and Italy. It is an unfortunate inconvenience.
Given that you have tickets covering the whole route that you plan to take you can travel. Just take the trains you intended to, and show your tickets to the conductor when he passes.