The "Advanced Dining Reservations", which used to be known as "Priority Seating" are not reservations in the true sense of the word. The only real restaurant reservations are at Vicotia and Albert's, the Luau, and HDDR.
Everything else is kind of like FastPass. Effectively there are two lines, one for people with ADRs and the other for Walk-ups. If you have an ADR they ask that you be there about five minutes prior to the scheduled time. For various reasons I have sometimes arrived as much as an hour early, or as much as an hour late, and these were still honored. Basically if you are on the walk-up line you will generally have to wait until there is nobody looking for the same size table on the reservations line.
I have sometimes had to wait for as long as a half hour after my arrival time to get seated. I have also seen times when they have closed the walk-up line.