Show me the amplifier that is not. potentially, an oscillator and the oscillator which is not an amplifier. If there were no amplification, there would be no oscillation. Have you never constructed an amplifier which, when you turned your back, would not oscillate or, at least, squeg.?
The magnetron is just like a klystron where the beam goes in a loop, passing the cavities again and again.
It's horses for courses - I, like you, have only dealt with Klystrons (UHF TV) but the theory of bunching and amplification is just the same. Linearity is not a problem with magnetrons as it is with Klystron amplifiers.