Does gilgobble/dajarte/wol damage affects testament's heal?

I can't speak for testa heal but when I tested my sama with hcb up and a gilgobble xtal to see how differently it affects certain procs in my case the double attack from gilgobble didn't lower my heal but lowered the chance to proc the heal from hcb and it also lowered my auto atk proc from muramasa, all I can say is double atk 1 from gilgobble becomes a priority auto as it is of the basic proc compared to testa, hcb, mura etc they all require a certain amount of auto to proc effectively in my case it proc double atk 1 way more then hcb heal and muramasa proc it hindered me all tho I did proc auto issen but at a much lower rate but it didn't cancel out auto issen completely as some people say it will overide any other proc completely, but it didn't in my case I'm only speaking from my sama experience using gilgobble & hcb which is kind of similar to your case with testa and gilgobble. Do not hold me to this info as like I said its through my personal experience I was also using auto5 on add at the time also, don't know if this helped but its my input on this matter and it seems no one else wants to share there experience so I thought I'd drop what ever info I had to you.

I use tests and the only thing that effects it has been the orange damage when attacking wol/daja can proc with it, I wouldn't suggest gilgob because there are more beneficial xtals

If you put it on testament it does over ride it XD