Installed Flash still getting interrupted with out of date message Safari Mac

Most browsers are blocking Flash content by default.  Most websites that require Flash have JavaScript on the page that attempts to detect Flash Player.  In olden days of yore, if Flash Player wasn't present at page load, that was because the person visiting your site didn't have Flash installed, so you'd tell them that they needed to update or install Flash. 

In 2020, it's far more likely that the person is running a browser that blocks Flash from loading, but since nobody has updated that website since 2009, it's providing you with vintage advice on how to fix the problem.

In reality, you probably need to enable Flash in your browser: 

https://helpx.adobe.com/flash-player.html

If the site is trying to infect you, it will keep trying, even if you update. (you did the right thing to go to Adobe.com)