Usually if you buy a bike from them, the fitting will be included in the price.

I wouldn't worry about "H". However, if you feel comfortable with the other shop that did the fitting, I would mention to your fitter or the supervisor that you were confused with what shop does what, and tell them that H got you confused. And leave it like that. That's how supervisors/shop owners know if there's problems with the employees. If they don't hear stuff like this, they think everything is okie dokie.

IF you are uncomfortable about the fitting and they seem to brush you off...find another shop. What matters to you is YOU. Ignore the personal part of it, it's business.