When I click the Generate button in this form, it opens the help site twice when finished. Probably something wonky about my environment but thought I should pass that on.
The Generate dialog Shell Executes the URL when done. That only happens once though - I suspect that there's something else in your shell perhaps?
What if you do this from powershell which should do the same?
start <PreviewSiteUrl>
+++ Rick ---
As a baseline, here's a picture:

I opened a Terminal from DM and executed:
start http://localhost:5210/apidocs/
and I only get a single browser tab, as expected.
And you're sure the tab wasn't open previously? It'll open a new window every time you run the generate cycle (can't control the window with Shell Exec).
FWIW, I'm not seeing that here.
+++ Rick ---
I made a little video. I'll send you a link to access.
I sent a OneDrive share link but also put the file on my FTP server in your home folder.
I have no idea what would cause that. I can't duplicate that on any of my two machines or my server.
This is with stock templates, right? Not some script running in the browser that might be opening another window?
+++ Rick ---
I'm not doing anything that fancy. 😃
It's no big deal and honestly not worth the effort to hunt down.
Found the problem - should be fixed in the next update.
Operator error! 😄
It was actually doing that to me too - I just didn't notice.
+++ Rick ---