Maybe I will learn basic rumba walk to control my feet better later . I wonder why it moves on the second ,third and fourth count ?

She had better not be counting... because if she is, she's going to substitute her own interpretation for her following her partner's movement... DISASTER. Being on time is far more about heading towards a future goal at the resolution of some structure in the music than doing every action by the metronome.

This is the difference between latin and smoove, the lady is free to express herself and flirt with her partner and the audience.

I am guilty of saying I let the man count. If I count, I cannot follow the ever changing count of my partner. Example, in the waltz chasse, sometimes he counts correctly one two and three but usually just walks through with the same beat on all steps, not holding the two. So I try to "glue" to him and follow whatever timing he decides to execute at the moment. He is not at all consistent. In the quickstep we have taken lessons time and again with the teacher giving him the correct timing on certain steps but he varies from what the teacher says.
So we women sometimes say "I will follow the man's count" because with an inconsistent partner I must somehow appear to be "with him". I am amazed at how much easier it is to follow men who consistently are on beat.

If you have a regular partner then you should discuse with your teacher about you keeping the timing. Its rare for two people to here the exact same timing. I dance at the championship leval ,but I still find it best sometimes to go with my wifes timeing in the waltz where as in the foxtrot she hears the rhythm as slow.qick.slow. and would dance it that way if I let her. But strangly when its her favorite foxtrot she will be right on time. The problem with a lot of men is that it hearts their pride to let the lady keep time and feel that they are no longer leading. Dancing is a lot more about following than leading ,to me anyway.