Negative frequency deviation in crystal oscillator
You’re overthinking it. In terms of the 1st plot, a positive deviation simply means that the crystal is oscillating too fast. Negative, too slow.
Generally though you’re correct. The Allan Deviation plot at the bottom doesn’t care about the 1st order rate (i.e. the frequency offset). It is a statistic used to characterize the frequency stability, or performance, of the clock across averaging intervals (τ).This statistic allows you to inspect the short/long term behavior of a clock, as well as the oscillator’s constituent noise types.