I made a few attempts going different ways.
My scenario notes, I wanted to be thorough with what I tested and noted down incase I missed a case...
user2 shared full access to user1. All calendars were blank before connecting to Outlook. Shares were setup before connecting Outlook. No actions were performed in Outlook in my testing except switching to calendar view and connecting to User2's calendar from Outlook account settings. Every event came from webmail.
Outlook logged in as user2, Webmail logged in as user1, added calendar event from user1.
Outlook logged in as user2, Webmail logged in as user2, added calendar event from user2.
Outlook logged in as user1, Webmail logged in as user1, added calendar event from user1.
Outlook logged in as user1, Webmail logged in as user2, added calendar event from user2.
In all cases the event created from webmail showed up in Outlook automatically while I was sitting in calendar view, so that I did not have to click anything to see the new event. All events came in as quickly as ~4 seconds and some took about ~20 seconds, this delay is completely up to Outlook, we send outlook a notification within a second or two of a change.
If you got a reproducible scenario on a test environment I can try these same steps I did in your environment to ensure I'm replicating correctly that would also rule out anything we have in our internal builds.