They know that they have to do this in order to get ahead. If they would show that they are aggressive and assertive all the time, it may bring them farther away from their goal. They are being submissive because they know that this is the best way so that they will not get noticed.
This is the best way so that they can get ahead of the other people that they are competing with. This means that they are submissive because they have planned it. Take note that a Machiavellian will not do anything that will not benefit him in any way. He knows that it will be beneficial for him in the long run.