I guess it didn't make sense since f_beat can be arbitrarily moved, but the beat is taken around the PSL freq ~ 281.73 THz. Attachment #1 shows the overlapping tau allan deviation for the exact same dataset but using the python package allantools, where this time I used the PSL freq as the base frequency. This time, I can see the minimum fractional deviation of 1.33e13 happening at ~ 20 seconds.
Quote: 
what's the reasoning behind using df/f_beat instead of df/f_laser ?

Another, more familiar interpretation
The allan variance is related to the beatnote spectral density as a meansquare integral (the deviation is then like the rms) with a sinc window.
