Does personal hotspot use any data when iphone is on Wi-Fi?

My iphone is connected to Wi-Fi, but is being a hotspot for my computer.So, I'm not using any data at all, right?

I doubt your phone's on Wi-Fi. On every phone I've tried it on (3 so far from 3 different companies and 3 different carriers) the personal hotspot feature or app forces the phone to connect to 3G/4G. If you activate it when the phone is on Wi-Fi, the phone will drop Wi-Fi and switch to 3G/4G.

If it didn't work this way, what would be the point? All you would be doing is having your phone make a second Wi-Fi network, when there was already one available. Why wouldn't you just connect your computer to that first network?