If the auto-scheduling is enabled for the template, then the properties (Update > Properties) in the destination Shell Schedule Sheets (with the same name as the template Schedule Sheet) will be updated. That is to state that the destination will also have automatic re-scheduling enabled and refreshed to reschedule the Activity Data.
If the auto-scheduling is disabled for the template, then the properties (Update > Properties) in the destination Shell Schedule Sheets (with the same name as the template Schedule Sheet) will be updated. That is to state that the destination will also have automatic re-scheduling disabled.
The Start Date, Duration, or Finish Date of particular Activity can be changed upon template push, but because auto-scheduling is disabled, none of the changes will be reflected in dependent activities.