Civilization Board Game - founding cities gives army extra move?
Those units can still move their full Travel Speed during the Movement Phase.

In the first paragraph of the rules regarding movement on page 19, the rulebook has this to say (emphasis mine):


  During this phase, each player, in turn, may move all of their figures, one at a time.


The rulebook doesn't go on to restrict which units constitute "all" units. Given the verbiage here, you should be able to move any units that were displaced when a city was built. The rules are also pretty explicit in that a unit can't split its movement points to perform other actions:


  Once a figure has begun its move, it must complete its move before any other figure may move.


So you also wouldn't subtract movement points from those units during the Movement Phase.

The rule you quoted ends by saying that the units have to go where "they can legally end" their movement. This is meant to prevent units from being able to end a turn on an illegal space should the player decide not to move those units during the Movement Phase.