Hi @Lauri ,
Thanks for visiting our forum.
For your requirment of the update time of Office 365, based on my research, Microsoft only provides the update history(listed by date) and we couldn't find the specific update time of day.
Also, as I know, the update process would run some steps(detect, download, apply), and the process may be interrupted by a temporary loss of network connectivity or others, which seems to make it more difficult to confirm the specific time of your update.
As a supplement, in the point of Outlook client, if you are worried about the future update would affect your other program, if it's possible, it's suggested to disable the automatic update(File>Office account>update options>disable updates) and mannually upgrade it for your need.
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