First of all, your tutor's explanation is absolutely CORRECT!
When you reflect an image over the x-axis, imagine you're folding a piece of paper in half from top to bottom. Remeber the x-axis is the horizontal line, therefore if you have to reflect anything over this axis, its going to be from one side of the origin to the other side. One side is the positive values of the y-axis and the other side is the negative values of the y-axis. So if you're going to reflect anything from the positive side to the negative side, you simply change it to the negative (that is multiply by -1, or negative 1).
So the coordinates with points given as (-2, 2) would be reflected over the x-axis as (-2, -2). The y-coordinates will change from positive to negative (or negative to positive)