In Settings->Schedules, if "Apply to Season" is "All Seasons", then the controller will change season according to all the seasons.
If Apply to a specific season, then that run is applied to that season only.
For example, if you have 4 seasons, spring, summer and fall defined, and schedule A is applied to all seasons, then schedule A will change when seasons change.
If you have a schedule B that you apply to summer season only, schedule B will run during the summer.
Make sure your seasons' start data and end date cover year round and they don't overlap. If there is a gap, the controller won't water. If there is an overlap, it'll follow the 1st one.