In the Lorentz Ether theory the same thing takes place, we see the other guy as being shorter and slower than you are, if all observers synchronize clocks in their reference frames by Einstein signalling method, a.k.a Einstein synchronization.
That means, that moving observer is actually shorter and slower, than one that is at rest in the Ether. However, if moving observer synchronizes clocks in his frame by Einstein technique, he would measure, that clock a rest is ticking $\gamma$ times slower and measuring rod at rest is $\gamma$ times shorter than his own.
Please read the following papers:
“Full simulation of SR by classical mechanics”. All effects and paradoxes of the SR are simulated in aquatic medium (universal frame), including time dilation, Lorentz transformation, relativistic velocity addition, twin paradox, mathematical formalism e.t.c. https://arxiv.org/abs/1201.1828
Chapter 3.5.5 - A Comparison between Lorentz's Ether Theory and Special Relativity in the Light of the Experiments of Trouton and Noble
That makes these theories empirically equivalent, as the article explains:
However, measuring technique by means of Einstein – synchronized clocks is not the only way to measure time dilation. Actual experiments have been conducted, and in these experiments researchers measure time dilation by means of the Transverse Doppler Effect.
Imagine that two observers rotate around a source a radiation in a circumference of very large diameter, let’s say many light years in diameter, so they are almost inertial. If they send a beam of light through the center from one point of the circumference to the opposite one, they would measure no time dilation, i.e. any Doppler shift.
Neither rotating ones, nor purely inertial ones that momentarily coincide with them would see any Doppler shift, since their clocks dilate at the same magnitude.