You are overdriving the amplifiers into non-linear regions, and they take a while to recover from saturation.
Tek scopes have a lot of overhead and recover well. Cheap modern digitising scopes are nowhere near as forgiving; if
any part of the waveform is "off the screen", then be wary of what you see on the screen

The scopes with the best overload recovery are old scopes with sampling bridges in their front end. Except at the sampling instant, the amplifier is not connected to the input, is not being overdriven and so does not need to recover.
Summary: you are seeing normal operating behaviour. Congrats for testing and observing and questioning your understanding of the instrument.