The initiative rules state that units that being the turn mounted do not get an movement/activation this turn. Them dismounting during the turn doesn't change this. The movement as part of the dismount is the only movement they get this turn. They do not get to dismount (as part of the transport's move) and then move again on their own, because they don't have their own move this turn.
Mobile vs. Immobile (p. 32)
At the end of the paragraph insert the following:
If a unit begins the Movement Phase unable to move on its own, whether it is immobile, shutdown, or being transported, carried or
towed, the unit does not receive a movement this turn.