Should my septum move on the inside of my nostrils when I breath out?

This is not a common finding after septoplasty. I would  suggest you see your surgeon for an evaluation.   Its possible that your septum has been mobilized to allow repositioning and its still mobile during the healing process.   

Typically the septum does not actually move with respiration, at least not visibly. Do you recall whether your surgeon removed any of your septum during your surgery? It is possible you could have less cartilage than you did before surgery, which might let the mucosal lining of the septum move a bit with respiration. You should go in to be examined for a good intranasal exam to have this assessed. It may not need any intervention if you are breathing okay, but it's worth being evaluated properly with physical examination.

Dear Keen4, I would suggest that you see your surgeon for a follow up appointment. After an intra-nasal examination a proper diagnosis can be given. Best regards, Michael V. Elam, M.D.