What you’re after is a “platform mount”. The print sits in an aperture and is sandwiched in place by a backing board and the front window mount. 100% reversible and conservation standard.
It’s suitable for most work as long as it’s not too big/heavy (the piece can sag in its pocket, but most framers go for a standard hinge as it’s easier and uses less materials.
You shouldn’t hinge onto the window mount though, you should form a ‘T’ with your hinging tape and attach it to an acid-free backing or barrier board.
The choice of tape should really be dictated by the weight, value and material of the piece. Linen is used for most work, but it’s generally much stronger than paper, so if the picture jumps off the wall, the paper can rip. The tape should be chosen so it fails before the paper.
The method your framer is referring to sounds like float mounting – this leaves all the edges of the art visible, but it’s not 100% reversible unless you use starch paste/tissue hinges.