If the browser is closed, and an Ad pops up or you click a url link in another app, whilst you expect the browser to startup and open that link in a new tab what it does is that it doesnt. It instead just returns to your last website from the previous session and disregards the request for the new link you clicked.
You didn’t mention your environment and browser version. I also assume you have “continue where you left off” enabled?
I tried this scenario on Android 10 with Brave-beta (1.11.93) … also tested Brave-Dev (1.12.88) on openSuse Tumbleweed Linux and do not see the issue.
Android 10 running Brace 1.10.99 Chromium 83.0.4103.116. Maybe thats why i encounter the issue let me check with later versions.