cross-product sign in surface integrals

Question

I read in some lecture notes I've found online that, when calculating the cross product in a surface integral when it comes to flux, I need to check to see if the vector that results from this cross product has the same direction of the unit vector that informs the surface's orientation. Otherwise, the magnitude of the flux will be correct, but the sign will not. This makes sense, but I don't get how I should check if the cross product has the right direction. I mean, perhaps is ok when the parameters are in a plane, because you just have to apply the right hand rule, but when, for example, the surface is a sphere of radius a, and the parameters are phi and theta, how am I supposed to verify this?