"Transition frequency" seems to be a common source of confusion here. In the context of the SI definition it means "frequency corresponding to the energy difference between the two states". This is the frequency of radiation that can _most efficiently_ drive transitions between the states. How fast the atom transitions between the states depends on the frequency, polarization, and power of the driving radiation and can in principle take any value. To avoid confusion this is called the "Rabi frequency" in atomic physics.
I had no idea how Cesium clocks work, other than the SI definition of a second is 9xxxx transitions between two states of a cesium atom.