Lookin good! Nice color.
To answer your question, no - the tint will not affect your auto-dimming mirror. A light sensor in the mirror compares the amount of light reflected around it / the mirror to the rest of the light in the cabin. It then uses an electrochromic gel to darken/lighten the mirror's reflection to better match the rest of the ambient light around you. So if you have a tint on your rear window, it will simply let less light in. This in turn will not do anything bad to your auto-dimming mirror, it will just dim less because less light is passing through the rear window and meeting the sensor.