This is common and expected for this type of door. The panels are set into the frame and are loose to allow expansion and contraction. The primer is cracking along this line because there is movement of the panel.
Don't try to glue or seal the panels to the frame. Cracking of the panels will result from them not being able to move.
Since you have nice stripped clean doors spraying is the best choice for primer and paint application. If you can't spray try to apply a thin controlled coat near the gaps, this will look better than filling the gaps and allowing them to crack.