Genos was already S-rank upon entering the Hero Association. Amai Mask couldn't stop his promotion as he was never promoted from A-rank to S-rank in the first place.
I couldn't understand the logic behind promoting Genos who is just a newcomer in hero association and manages to get into the highest rank in just few episodes. In Episode 5, The Hero Association interviewed Genos about the House of Evolution's destruction and upon confirming that Genos played a part in it, they made an exception and gave him the rank of S-class based on prior experience.
And I don't see why Amai Mask has to keep his plan while knowing that there's a rule to promote a hero to S rank in instant. Again, it's not promotion. Promotion is a change of rank from a lower rank to higher rank. Genos is initially S-rank so no promotion took place. He was not initially assessed as A-rank. Amai Mask maintains his plan to prevent those heroes initially assessed as A-rank below from climbing into S-rank. This might not be stated in the manga but I see this as his way to prevent diminishing the standards on what it takes to be an S-class hero, although he does acknowledge a few heroes not in S-class.
It's by his choice that Amai Mask maintains his rank as A-class Rank 1. The difference in ranking does not immediately mean that Amai Mask is weaker than Genos. Example being King, who's S-rank but is weak and Saitama who's B-rank but is probably stronger than most, if not all, S-class heroes.