I recently discovered an issue with my exchange calendar not syncing with my Iphone correctly.
I could update my calendar from Outlook, check it in OWA and it was correct yet my Iphone still hadn’t updated causing old calendar items to alert me.
There are two things you need to check to ensure you Exchange calendar push syncs correctly.
Firstly your calendar will only push sync if it is set to be the default calendar,
Settings -> Mail, Contacts & Calendar -> Scroll right to the bottom under calendar and ensure the default is set to your work account.
Secondly is to turn ICLOUD off for calendars (this was my issue).
Settings -> Icloud -> de-select Calendars
This causes a massive delay when updating your calendar which is the issue I was having and it caused old items to still be displayed and alerted on my phone
It took my quite a while to find information around the Icloud issue, It seems your calendar push syncs and Icloud takes a long time to update your calendar, I turned it off and my calendar immediately updated and has been working perfectly ever since.