Sounds like you're doing it correctly. One tip is to start with fairly clean cuts on each end of the mylar. If it is already seriously frayed, it won't look good at the head of the fly. So...start with a clean cut, push it just past the eye of the hook (1/4" or less usually works fine) onto the shank, and then tie it in there. A couple of loose wraps, slowly tighten, then several very tight wraps on top of that. At that point I spread a drop of glue over those threads to hold them in place, then move the thread to near the hook bend. Invert the tubing down over the hook shank, and tie off.

One thing I've also started doing to help the fly have some "body" under the tubing (medium diameter), is to cut the marabou long, and wind the excess up the hook shank.

Also...for some reason the pearl mylar tubing seems to invert more easily than the silver. It seems to be because the silver is a stiffer material?