You have it reversed.
Tape is stored tails out precisely so that the echo is POST signal. Any pre-echo is from when the tape is not in an "already played" orientation.
Tape print through is determined by other factors besides the orientation of storage. Notably, fluxivity level of the record amps along with how loud a particular sound is printed. Thickness of the tape is also an issue. You almost never get print through on a multitrack as the tape is a lot thicker than 2 track tape. But there is also different thicknesses of 1/2" and 1/4" tape. Also, the speed used is a factor. A 30 IPS tape will have the pre-echo much closer to the signal and be harder to detect than the longer distance of a 15 IPS tape.
A 15 IPS 2 track tape of very long length (thinner backing) and having the machine set up at +6 or higher flux level, with a loud event that pegs the meters and then rewound a few times to sit heads out, is a worst-case scenario.
Most of what we hear at home on vinyl is groove echo. It can heard as pre or post. Good engineers manually open up the pitch before a loud event to add land to protect against this. I have also gotten post-echo when the calibration on my lather computer was off and packed too tightly immediately after, say, a loud, cold ending. You don't get much audible groove echo unless the signal requires a large groove modulation preceded or followed by quiet. Like tape print-through, groove echo is always there but at varying levels and mostly masked by the program.