I'm not sure if I understand correctly, but yes.
each accout logs into a mailbox using its username/password(/mail server) combination and downloads all mails from there. If you forward mail from mailbox2 to that mailbox, also mails from malbox2 will be downloaded from mailbox. And again from mailbox2, when the second account will check for mail.
You should remove all forwarding. It has no meaning first to put mails together and then to separate/filter them.