Your understanding sounds pretty accurate. Let's say there is a 4 player draft:
pick 1: team a
pick 2: team b
pick 3: team c
pick 4: team d
since team d picked last, they get the #1 waiver priority. team c gets #2, team b gets #3 and team a gets the last priority, #4.
When a player is on waivers, the team with the #1 waiver priority gets the first shot at adding the player. So, in this example, if team d does not add a player, team c gets the next shot, then team b and finally team a.
Now, lets say that team c makes a waiver claim on cueto this week. Once they make the claim, they go to the end of the waiver priority list, so the order now goes:
So, the only way for you to improve your waiver priority standing is to not make a waiver claim, while people with a better waiver priority make waiver claims.
Adding a player that is a free agent, and not on waivers, has no affect on the waiver priority ranking.