Nope, does not mean a "transmission" problem necessarily. I mean it could be but more than likely ,not. Todays cars are governed by their computers. If the computer is getting a "trouble code" from one of the various sensors that an automobile has such as the Map or Tp sensor, it will signal the transmission not to go beyond a certain rpm or shift point. Some shift into second, some shift into first it all depends on what the manufacturers "limp" mode has in its algorithm.
It could be argued, no matter what sensor is causing the problem, the transmission is not working. The sensors are part of the operation of the transmission.