I think it's possible it's happening when SF is checking Scheduled downloads, possibly when SF isn't open. (I'm not sure how it normally handles scheduled items, though, whether it checks only when SF is running or checks regardless.) And because my PC is kept running 24hrs/day, it's possible they're simply opening during idle time. BTW, SF is not set to automatically launch on startup.
The persistence part is odd. The window for "you have an old version" was still onscreen after SF closed. And when I closed it, the second window trying to sell me more SF software replaced it. Unless someone else has an idea, I suspect only the developers can answer why and when these pop-ups are appearing. I'll probably submit a Support Ticket.
It could be the scheduled downloads, as I never scheduled downloads. And you came up with the best idea: to contact SF support. I think several members (maybe more) have been having overall issues with scheduled downloads. I can see its use if people download episodes from several different providers. I get shows from Amazon, and what happens is when one show is on break, another soon starts up, and I just wait till Friday and download the 5 episodes manually for that week, and most times it's only one show as the others are on break. Then one goes on break, and another starts more episodes. I have seen people have way too many issues with newer versions and scheduled downloads to where they even disappear from streamfab but stay in Task Scheduler.
But even you can confirm it's not happening when a user starts SF manually. I did recall after again looking at your screenshot, I had it once, I think it was after doing a full clean of SF, similar to a clean installation. But it went away and never came back. Mine, I think, wanted me to get the Fandango Downloader, and I also have access to all modules already. I never though seen the "you have an old version", but I know what members to fully trust and know that SF, in an unusual move, disabled pretty much any version older than 6247.
And for $10, I am not happy now with their extended download with missing versions.