Overload in tape at higher than normal operating levels is due to tape saturation - this is separate and distinct from tube distortion. The VU meters on tape machines don't reflect the pre emphasis either in the bass or high frequencies, so it is up to the engineer to 'know' how to set levels to accommodate this. Also, VU meters were
average responding devices and would be rather blind to transient peaks. If there was for instance a flute solo and during it a big bass drum hit, the flute could take on a very audible 'fluttery' quality from saturation.
Tape playback preamplifiers have, due to the reproduce EQ, up to 40dB or so of feedback from that source alone. RIAA phono EQ is similar. These EQ curves don't
have to be implemented in feedback, but in tape machines that is the way it was mostly accomplished. Due to the nature of the EQ curves, the low frequencies have the least feedback, and the high frequencies the most.
IM distortion is usually not spec'd for tape machines, probably because it would look pretty ugly. Tape, by its nature suppresses even order harmonic distortion so what remains is almost totally odd order distortion (in a 'perfect' machine this would be totally the case). The typical harmonic distortion of tape at normal operating levels is about 0.6%.
Since the distortion products are mostly low-order, the ear doesn't hear the distortion as such, at least at levels below saturation. On direct comparison, tape verses digital is totally obvious but that doesn't keep tape or vinyl from sounding very, very good.
This is a graph I made awhile back which compares the 1kHz harmonic distortion at normal operating levels between tape and vinyl. The tape machine was vacuum tube.
https://drive.google.com/file/d/1FoPWw0pe_5L6rZk8qBSa0rLDQtDv8fOz/view?usp=sharing