I've built the prototype of the 20 MHz variant. In that one, the oscillator runs at 20 MHz, which means that the digital section has to be powered at 5 volts and the output actually comes from the ATTiny's timer 0. The board has a pair of DIP switches that allow you to select from 4 different output frequencies. I've run the board for 12(ish) hours to get an allan deviation from it. At 10 MHz the ADEV is (nominally) the same as I've measured in the past. That holds true for 100 kHz output as well. So it's clear that the controller acting as a clock divider doesn't have any impact (good or bad) on the stability of the output.

The bad news is that I made a design mistake and needed to tack a wire onto one of the DAC pins to connect it to the correct power supply. So the boards I have aren't going to work. Additionally, I'm not fully satisfied with the power arrangements. The 5 volt input power goes directly to the digital section with no regulation. I'm not sure I'm willing to trust the average wall wart that much.