Outlook app updating even if Background refresh disabled

Please check whether you have mail app listed below Background App Refresh.

What you are referring to is "Fetch" and "Push" emails. The setting for this is available under Password & Accounts. Refer to the GIF below

You may know that there two settings (Fetch and Push Mails)

Google, AOL, Yahoo - Only Fetch mail Option is available

iCloud, Exchange, Outlook - Both Fetch and Push Mail option is available

1. Push Mail: Whenever possible the email client will push mails to all your devices.
2. Fetch Mail: You need to set How you want it to be fetched, Automatically, Manually , Hourly,Every 30 mins, every 15 mins
   1. Automatically: will fetch when the iPhone is powered and on WiFi
   2. Manually: with fetch when you open email, open Inbox and swipe down
   3. You get an email notification as soon as the client server receives an email and your device is connected to internet, irrespective of whether the mail is in your device's Inbox or not

I would request you to use iOS mail app and configure Outlook. I do not face any such issue. However I would download Outlook app and see if anything that you may over overlooked without doubting your competency. I will revert surely with my findings.

Meanwhile here is a GIF for iOS mail app.