First let me say I don't use ASB - Personally if a site is suspicious, the last thing I would want to do is whitelist it.
So that shouldn't the case - even if it were I would think there would be many posts related to this.
Also the exclusion would likely to be in the Avast Web Shield component settings and not ASB settings (perhaps why you can't find it).
I have no idea of what Upgrade you are talking about, as far as I'm aware there isn't a paid version of Avast Secure Browser, so it may be offering a paid version of Avast Premium. Which as far as I'm aware wouldn't change the fact you are getting an alert.
What is the URL of the site exclude the httpx elements (just the domain name), better still post a screenshot of the Alert window with the details option selected. Then someone can investigate the site.
What happens if you try to connect to this site using a browser other than ASB, I suspect you would get the same alert.