The '_check' function in 'Check Action Rules' scheduler checking a condition before executing the process. That condition checks whether the action date greater than last automated action run datetime and less than of current datetime. Whenever the '_check' function executes it saves that time as last run date. So that's why when we run the scheduler manually by putting back date, it is not executing process. 

Odoo V16: addons/base_automation/models/base_automation.py:563: def _check(self, automatic=False, use_new_cursor=False):

if last_run <= action_dt < now:
try:
action._process(record)
except Exception:
_logger.error(traceback.format_exc())

##For testing you can modify the code as 

if action_dt <= now: