Emitter followers as Colpitts oscillators
Emitter followers are well known for being prone to oscillation if they're feeding a capacitive load. The trait is shared however, with source followers, cathode followers ( Remember vacuum tubes?? ) and many op-amp output stages, all for the same basic reason.
There have been lots of articles and write-ups about this issue, often with sophisticated circuit models and accompanying mathematics, but the basic issue is easily grasped with just a little intuition:
Every follower is just one inductance away from being a Colpitts oscillator.
Ideally, you would want to reduce the amount of capacitive loading, but if you can't do that, then sometimes, the best way to suppress follower oscillation is to lower the Q of the unintended tank circuit, perhaps as sketched above.