They're checked one at a time in this order. QA>TA>DA>AM3. So adding double attack actually lowers your AM triple attack rate. Although DA+ is still overall DPS increase, just a tiny one.
Here's the best explanation of AM3/multihit interaction I've seen. http://www.ffxiah.com/forum/topic/31767/is-a-mythic-even-feasible-anymore-for-a-newbie/2/#1941496