Your reasoning starts out nicely with y=Ax, but you get the wrong conclusion. The layout of x and y are not affected at all by row or column order, they are just consecutive numbers in either case. So you have to look at the layout of A.

For the row-major layout the multiplication Ax ends up being more cache-efficient than for the column major layout, as for calculating each component of y you need to scan x and a row of A.