I think you may have some convex faces.
Here I give an example of a bevelled vertex on a cube. Notice the face circled in the first image (I use this face as its the most obvious, but they will probably all have, to some degree, the same issue), looking from an acute angle (middle), you can see the face is not flat, an easy solution is to select the two vertices as shown in the last image and CTRL + J to join with an edge to make triangles.

You could select all the faces and CTRL + T to triangulate all the faces at once, but you will have to check the edge is added perpendicular to the angle of the curve.
Hope this helps.