This also transforms like a vector for us. For example the derivative of a scalar function , is a 4-vector. We do need to be careful about the sign on the time derivative. In GR, we keep track of the signs using the metric tensor but we do not wish to introduce this complication here.
We choose to use the crutch to keep the calculations simple for now. If , one can see that introduces a sign change due to the in the denominator. (In GR... vectors can have upper or lower indices and we use the metric tensor to raise and lower them.)