Hope it's not too late but the condensed version is: every surface in a 3d program is created by a polygon defined by edges. But those polygons REALLY are defined by a bunch of triangles, you just don't see the secondary edges. When you export, some programs might break the polygon into triangles differently than program in which you modeled it, so it can stretch over the concave part of the polygon. There's two solutions to this: either, before export, triangulate the model (turn those virtual triangles into polygons, usually there's an option for that in the export settings), or keep sure that any polygon that has more than four edges is both flat an convex, then there's almost no importance to how the triangles are generated. Triangulation is more preferred since in bunch of advanced cases how the polygon is being triangulated is very important.