In Pandemic, can the Containment Specialist remove more than 1 cube (without the action of treating) in a cured city?
The key verb here is treat.

From the game base rules (emphasis mine):


  Treat Disease:
  
  Remove 1 disease cube from the city you are in, placing it in the cube
  supply next to the board. If this disease color has been cured (see
  Discover a Cure below), remove all cubes of that color from the city you
  are in.


The Medic can remove all cubes from a cured disease simply by entering it but it's his role privilege, other roles still have to spend a second action to cure all the cubes


  MEDIC
  
  The Medic removes all cubes, not 1, of the same color
  when doing the Treat Disease action.
  If a disease has been cured, he automatically removes
  all cubes of that color from a city, simply by entering it
  or being there. This does not take an action.


For instance, the containment specialist drives to Atlanta where there are 3 blue cubes (1 action). By doing so, he removes a cube for free, but only one since it's not a Treat action. Then he treats the blue disease thus removing the remaining two cubes (1 action)


  CONTAINMENT SPECIALIST
  
  When you enter a city with 2 or more cubes of the same color, remove 1 cube