IMO I think the reason most sit and wait for them to take a run is to reduce the chance of the fish noticing that you are pulling the tipup up in order to grab the line. I do sit and wait for a few minutes. If nothing happens I do release some more line from the spool before lifting the tipup. Then I use my fingers to "feel" if there is still a fish on. If there is, I set the hook. Now if they take a run before you can do all that, it makes it lots easier, just lift, grab the line, and set the hook. I have landed plenty of 8lb class walleyes that way.
That is my style when fishing for walleye. I use beaver dam tip ups, braided line (30lb), and a 18 inch mono (8lb) leader with a treble hook.
Matt