This is a very common question.
The bowing results from over stretching the screening material. Most better screen frame has a natural outward bow to compensate for the tendency of screen material to install tight. The best solution is to place your hand in the center of the screen while rolling the spline in. By doing this the screen cloth is pulled into spline channel from the outside edges and not the inside. Keeping your hand in the middle puts just the right amount of slack in cloth. As you finish the last third of the last side, ease up on your hand and the cloth will naturally firm up.
