"Normal" is one of those words where it depends on the individual and their circumstances. If you broke up several years ago with someone and you are still sad over it while having moved onto a new relationship it may mean you never really let go of that relationship on some level. This is common especially if the ex hurt you or they dumped you. We also tend to over romanticize the past!
Essentially if you are with someone else only because your ex chose not to be with you could stir up some emotions. Just because you are in a "new" relationship does not mean you are "emotionally invested" in it or "in love" with the current person. In fact it's not uncommon for the next relationship after a breakup to be a "rebound" relationship. Eventually with time you move on both mentally and physically.