The station platforms are located on one level; so you will change from one track area to another without having to use stairs.
If the arriving train is on schedule, then you will have no problem making your connection.
Also if the departing train is more or less as delayed as the arriving train.
If my first train is late and I miss the 2nd, will I be able to get on another train? How are Italian trains in keeping their schedule?
The Italian trains are usually quite good at keeping their schedules. For your journey, then you have good back ups if the 2nd train is missed with either more trains to Siena later that day or you have the SITA bus located next to the train station with direct buses to Siena.
Thanks for the help.