The new text of massive is:

1. After a Massive figure ends its movement in spaces containing at least one other figure during an activation, Start of Round, or End of Round, the Massive figure cannot move any more during that activation, Start of Round, or End of Round

Does it means that a massive figure can move only one time in a round? or only one time in each of this phases?

It means you can't move if you ended your movement on another figure. It's just to prevent people from pushing figures again and again during a phase

Before end of round was a loophole because there isn't an activation happening. Start of Round and End of Round are now considered to be "time frames" for the massive movement. if Massive figure ends movement on top of figures, it cannot move again during the same activation, the same end of round, or the same start of round.

A massive figure can still end movement on top of figures once during each activation, each end of round, and each start of round.