Application of floors and ceilings to the time complexity of loop with constant index increment
You are technically right, and if you want an exact value of the number of loop iterations, you can't forget the floor.
However, when doing asymptotical time complexity analysis, you can often toss terms that are negligible in front of other terms. In this case, $\frac{m}{a} - \left\lfloor\frac{m-1}{a}\right\rfloor \leq 1+\frac{1}{a}$ which is negligible in front of $\frac{m}{a}$ (for $m$ big enough).
See here for more details.