5.1.0 and 5.1.1 are currently available only via the Local Beta program. See Introducing Local Beta Group for more details.
If you download the Sequel Pro nightly, be sure it retains the name Sequel Pro.app and is in /Applications or ~/Application. Local detects if Sequel Pro is “installed” by using the following command:
find /Applications -maxdepth 2 -name "Sequel Pro.app"; find ~/Applications -maxdepth 2 -name "Sequel Pro.app"