Instead of basing your logic on the wording, you should actually test it. I just tested it, and I gained life with it. I did not have any Vampire on, nor did I take any damage for my Phoenix's Warmth to kick in. This game is horrible at descriptions, so taking them word for word is a mistake. Also, Ignite itself works in fire form, so why wouldn't its proficiency?
I tested it during the Drakomeyer (something like that) fight. Unless he has some kind of projectile that isn't easily visible, I was gaining life with fireballs. And I did sit there for about 3 seconds doing nothing, just to see if I gained any, and I didn't. The one thing I did notice though, was I only have 10% invested in this proficiency, and it appeared to be giving me life about 30% of the hits. If you can think of anything besides Vampire or Phoenix's Warmth that would give me life (besides healing myself, obviously), that'd be great. I hope I'm right, else I just wasted a bunch of points in Ignite. I'm going to further test it to make triple sure. It's hard though, because I have to make sure nobody is hitting me. Makes me wonder how Phoenix's Warmth works anyways, because as you're hit, does it immediately give you life? Shouldn't matter, as the timing would have to be extremely coincidental if I was gaining life less than 1 second after my fireballs hit.
After further testing, I would say no it doesn't, but I stopped putting points into it just in case, so I'm at 15% right now. With a 15% chance, it's entirely possible that several shots in a row wouldn't land. I did this a few times. However, I can't fully test it, because it's very hard to not get hit (and be 100% sure you weren't). Somebody would have to not put any points into Phoenix's Warmth etc., and then they could be sure. But hey, when I tested it before, I was at distance, and appeared to not be hit at all, and I gained life from this. I tried it a 2nd time on the same fight, and same thing. But then now I can't get it to do it, and when I do, I'm not 100% sure I wasn't hit. Very odd if this doesn't work, because Ignite "sets your weapon ablaze", but yet it works on both stances, so why wouldn't the proficiency?