The Mac is reading your computer live, so when it says up to date, it is. The phone app can miss the “now up to date” signal afterwards, so it keeps showing the old status. I’ve passed this to the team.
In the meantime it’s safe to ignore the phone’s update notice whenever the Mac shows up to date. Fully closing and reopening the phone app may also clear it.
One quick check so we’re looking at the right thing: could you confirm the phone app is signed in with the same account as your Mac app? You can see the account at the top of Settings on the phone.