Hello Matthew,
I test with a Mac on High Sierra version 10.13.6 and a Mac with the beta version of Mojave and they support push notifications. Outlook 2016 on Mac supports push notifications as well. SmarterMail does send off notifications to EWS clients who have subscribed to push notifications.
Open the calendar app and open the preferences menu. Under the accounts tab, click on the Exchange account you're interested in and then make sure you're on the account information tab. There should be an option called refresh calendars where you can choose push, every min, every 5 mins, etc. I believe the other sections should have a similar setting in their respective locations.
Regards.
Larry Duran
Software Developer
SmarterTools Inc.
www.smartertools.com