This is not normal. You are correct that fabric softener should be added at the spin/rinse cycle. Without knowing your exact model number, it would be difficult to troubleshoot - which could involve replacing the dispenser tray, the water inlet valves, or the control board.
A simple workaround would be to stop adding fabric softener to the tray, and manually add the softener to the rinse cycle - like I did as a kid. Other option is to use no fabric softener and use Downy (or equivalent) dryer sheets. Because this is a front load washer, you can't use a Downy ball.