Based on start of the month
For EQ I believe it's from when you enter. I think they mentioned on the stream that you should be comfortable with where you are and make rank ups before joining. For aw and aq I'm guessing it's a cut off just before the next event
EQ locks difficulty when you enter, so if you’re just about to hit a new progression or bump up a prestige tier for more rewards you can hold off starting EQ.
Not sure on AQ - I assume either start of the week it snapshots alliance prestige, but it could also be updated every day when a new map starts.