Aatrox and life steal items

So the cost for aatrox's w blood thirst is about equal to life steal so useing it would cancel it out the cost and heal. i just built and and i noticed when ever my blood thirst procced i didnt heal or lose any hp even with my 20% life steal from and 12% healing from the damage of my auto attack which is physical damage and 12% healing from my blood well which is also physical damage when building deaths dance . you can check in on minions champions monsters etc. idk whether it belongs here or in bugs catagory