When do you pay the cost?

I'm pretty sure I know the answer to this question, but it came up in a game tonight and I don't have it in my FAQ -- when do you pay the cost to use an ability in Tactics?  I think it's really only important with abilities that cost a health to activate, like AZ's "Thermal Shockwave".  Must he lose the health, and only if he's still active have the ability go off, or does the ability go off, then he loses the health which could then incapacitate him?

If possible, I'd love an official answer I can add to the FAQ.

You pay the cost upfront. If you pay your last health, you're incapacitated before the ability does anyone any good.

Thanks.  Going in the FAQ.