What’s the definition of auto-update for a Cask?

I see that the formula flash-npapi is labeled as auto-update. If I understand correctly this means that the Flash plugin should update itself independent of Homebrew Cask. However, when I hit the “update” button of Flash manager, it opens the web page to download. This is different from other applications (like VS Code or Chrome) that simply downloads the update itself.

Is there any response?

Since Flash will be depreciated in 2020, there is no reason to make a long term auto-update for flash. After 2020, there will be no option to download flash ever again.