POP Systems are generally accessed by using Outlook Express or Microsoft Outlook, or maybe Thunderbird.
Do you open a browser and go to, say, GMAIL, YAHOO, HOTMAIL? (That would likely be an on-line system).
Or do you start Outlook Express and do a SEND-RECEIVE? (That would be a POP system.)
Another way - can you go to a coffeeshop or a neighbor's house and use their Browser and then get to your Email System from their computer? If so, then you're using an on-line, not a POP system. POP Systems are pretty old-school when Mail Server hard-drives were small and they wanted to off-load all mail to all users instead of saving it as a centralized storage.
But can you reaffirm how these messages to old system originate? Are you creating messages to them, and then they're doing REPLYs back and those are being somehow directed (re-directed?) to this old system?
Since you haven't consolidated mail accounts into a central 'front end' account, then that eliminates one possible source of an inadvertent error (or programming error).
You might ask those correspondents how many addresses FOR YOU that they have. Do their address-books contain your new AND old address? If they could delete your Old Address from their book, let them originate a message to you, then you REPLY, then see if they'll send a RE-REPLY and watch what happens.