Is the fact on which the working of a cyclotron depends i.e. "The frequency or time period of revolution of a charged particle is independent of its ‘speed’ or radius of its orbit" consistent with the theory special relativity about which we learn in the Cyclotron's limitations that "It cannot be used to accelerate electrons because electrons are of very small mass. Thus, the ‘velocity’ will be increased to such a great extent that the electron will be thrown out of the step with the oscillating field." In one statement speed doesn't matter but in the limitations, it matters? How and why?

Is the fact on which the working of a cyclotron depends i.e. "The frequency  or time period of revolution of a charged particle is independent of its ‘speed’ or radius of its orbit" consistent with the theory special relativity about which we learn in the Cyclotron's limitations that "It cannot be used to accelerate electrons because electrons are of very small mass. Thus, the ‘velocity’ will be increased to such a great extent that the electron will be thrown out of the step with the oscillating field."
 In one statement speed doesn't matter but in the limitations, it matters? How and why?