"Cross-domain autologin asynchronously" doesn't log me in "instantly"

I have the “Load Cross-domain autologin asynchronously” option enabled in my Domain Mapping settings.

It redirects me to the log in page and after a few seconds it refreshes and logs into the Dashboard.

I assumed with that option enabled, I should just be able to select the sub site from the drop down and instantly go to the dashboard, without seeing the login screen.

But it doesn’t log me in instantly, it first takes me to the login page, waits for some time and redirects to the dashboard.

I have done a plugin/theme conflict test, disabled varnish and redis from my cloud server, but it didn’t make a difference. The debug.log is added in the internal notes.