The network software already notifies them via the StackExchange notification mechanism, on their return to any SE site. We can not force them to come to the new site and followup, and frequently those who are least familiar with the site don't understand they should login with the same login they used previously.
This is an oft-addressed issue and discussion amongst the moderators and SE team and on Meta.StackExchange (the network meta), but since this is a "people" issue and not a "technology" issue, there's very little to enforce here. All we can do is alert them, and encourage them how to do things properly.
StackExchange staff have been in a process of rewriting a fair bit of the user documentation to ensure that the less-frequent users of the network are better able to navigate easily amongst all the sites, and these things do take time to refine.
All that is to say "sorry, we can't stop them getting migrated and ignored, but it does suck".