There is no “additional” testing. A bug that presents itself only on install but not on upgrade will not be device specific. If you are making changes to code that could create this type of bug, like the SQLite database creation code, you should test installing on at least one device. This is not “additional” testing. This is the bare minimum testing that should be required before any proposed updated is released as stable.
Therefore, the designation of a new release as stable should be sufficient to make that release the one that is distributed on the website.