You are correct that on the 528T in the Drake, you will not get a proper refill unless the water from the refill hose runs down the overflow riser.
Which side is the hose popping off of? It should be relatively-easy to seat it securely on the valve head. Likewise, it should be attached to a metal clip of which you push the circular part into the open end of the hose and then you clip that to the top of the overflow riser, aiming the water into and down the riser. That hose should have a little play, but not so much that it kinks or flails around. It's easy to cut with a scissors.
If you're missing the clip or something, just call Korky at 1-800-LAVELLE (1-800-528-3553). They are very nice and they will happily send you a new clip or hose, usually for free, and they can talk you through hooking it up.
If you need me to take a photo of how the 528T in my Drake is installed, I'm happy to do so.
Here are the installation instructions from the Korky web site:
http://korky.com/PDF/528.pdf Look at item 5C.
Here's the installation video from Korky. The part about how to attach the refill tube starts at 1:16 into the video.
[video]http://korky.com/528.html[/video]
Good luck. Let us know how it works out.