There are several topics about the new upgrade app on the forum. Not sure about the manual but it is possible that it needs an update (there is already a first discussion: Reccomended way of upgrading. · Issue #44 · nextcloud/documentation · GitHub).
That is an excellent question how and when these messages are triggered. There are different release channels (see server settings in your admin-interface), so each release channel gets updates at a different time, e.g. production is more conservative than stable.
I’m on the stable-release channel and I get the notifications of a new update to 10.0.1 (make sure that your server can establish outgoing connections to carry out these checks). But I added some config-options to test the new updater app ( Test our new work-in-progress upgrader script).