I haven't used the app lately but there was a period where the website used your local time as the start time regardless of what you asked for. They fixed it after a week or so but it was super confusing until they fixed the GUI.
If something similar is happening the workaround until they fix it is to search the day before you want and keep asking for later times until it shows you the morning of the next day that you really wanted. Obviously way less than ideal but there's usually a workaround until they get it fixed.
Given how many people use the trains and willing Italians are to vigorously express their frustrations I'm sure Trenitalia is keep well informed when these things happen after an update. ;)
It wouldn't be Italy if everything ran smoothly,
=Tod