We have downloaded the recent patches and the Office 365 patches are popping up a "Updates were installed" window when complete. It doesn't look like there's a way to make the patches run in the background with no pop-ups.
This is the standard behavior of the Microsoft tool that Broadcom integrates with. We are not aware of a way to turn this off but will look into the possibility of improving usability in a future release, and we cannot make any promises that we will be able to keep the pop-up from showing.
If an expedited resolution is needed, it is suggested that customers escalate this issue to Microsoft.
Best Practices etc: Deploying Microsoft Office 365 updates with Patch Management Solution