If you’re changing folder names or moving messages frequently in web-client you’ll notice that Airmail delays from being updated which is the refresh timing is different from Airmail and Web-Client. But definitely you will able to set refresh time for per accounts in Airmail that keeps the folders up-to-date on time.
In the following screenshot below there is an option in the Preference which you need to change it for per accounts:
Airmail will obviously keep them updated whenever you set the refresh time. Therefore you’ll need to set the same option for other accounts if you wanted to do but we do not recommend them since because it requires more bandwidth which could cause issues with syncing.