Any paperboard would warp if exposed to certain conditions, whether 4-ply, 8-ply, 12-ply, or more-ply, and quality of fibers has little to do with it. For example, exposure to moisture would cause disoriented fibers and unequal expansion/contraction and warping. The only prevention of that would be a non-hygroscopic board, not made of paper.
Perhaps the most common cause of warped mats in frames is restriction of normal expansion/contraction cycles. That is, boards cut too large, without an allowance for expansion; or too-tight fitting that prevents movement of the materials within the confines of the frame. Springs in aluminum sectional frames often have that unfortunate effect. The revention of that is to make sure that all materials in the frame are free to move within the expansion allowance of the frame. Generally, if the glass can not be rattled, the fitting is too tight.
If a large, heavy paper artwork were hinged to the top edge of a window mat's opening, the gravitational stress of its weight pulling the top downward might cause the side margins to become wavy. The prevention of that, of course, is to hinge not to the window mat, but to a solid backing board, reinforced from behind if necessary.
It is important to understand that paperboard fibers will not compress, but will cockle; and they will not stretch, but will shred.
Prevention of causes is the only way to prevent warping of mats.