Currently 'Boost for Lemmy' doesn't show any real-time notification. The minimum check interval can be set to 30 minutes and that's also inconsistent. There should be an option or by default it should show real-time notification. This issue was also present in 'Boost for Reddit'.
Google and Apple both provide push notification services to avoid the polling problem.
But that would require each and every instance to register with each and every app for it to work, which is definitely not going to happen.