If your roofer has told you that the dripping edge must be between the gutter and the ceiling, you are absolutely WRONG. The dripping edge should always be in front of the rear edge of the rear gutter. Its function is to ensure that rainwater from the roof falls into the gutter and not behind it. Over the years, I have installed kilometers of fog-type, semi-round, K-type gutters, dripping edges, covers, etc., etc., and sometimes these gutters have to be installed with a lot of little fall.
Thanks for the compliments, but, no offense to anyone here, I don't think that placing gutters is rocket science, LOL. I'll probably eventually put them in my own house. I have a mix of copper and aluminum channels with a mix of semi-round and K-style channels. Let's hope the roofer doesn't hit it hard against the fascia, so the guy in the ditch will have the opportunity to put it underneath, without committing suicide in the attempt.
For example, a gutter of, say, 60 feet long could, in a sense, be installed almost perfectly level. The channel must be mounted on the face of the fascia, so that its path (which must be inclined towards the downspout) is below the dripping edge that flickers at all times. Yes, I know the small curve that kicks out, but in my experience it hasn't been enough to allow me to go up and down the gutter, at least not the material being installed around here. It says it uses a dripping edge with a very long vertical flange so that the bottom edge of the flange is well behind the gutter and prevents ice from accumulating on the roof.
He said that it contained a lot of water and that in winter it turned into a lot of ice and that gutters would fall out. The material that Dan T mentioned, we have also used, in fact, it works quite well on short sections of gutters, it works less well, in the long term on longer, sections of gutters, of 4 feet. It allows the tiles and the horizontal part of the drip edge to overlap the gutter, in accordance with standard practice. What your installer was contemplating was to let the bottom edge DE overlap the back of a K-type gutter (as I read it, the results may vary).
The gutters that go to the drains concentrate the water that drains on the roof and cause erosion where they are expelled. If wind-blown rain or a roof with a very low slope conspire to cause water to flow back below the edge of the tile eaves to fall down the side of the drip edge, it should be able to drip down the bottom of the eaves and fall into the gutter.