I can't set starting_time for the adset.
When adset is created, the start date is:
[start_time] => 2016-06-31T13:00:00+0600
which means the date has been generated by my code.
But then, when I read adset by id or observe it in ads manager, the start_date turns to creation date (today's one).
Has anyone faced this trouble?
Your syntax is correct.
but June doesn't have 31th... that's why facebook ignored that input