When using the Avast SafeZone Browser, does Malwarebytes Premium with real time protection enabled still block access to malicious websites? I’ve never noticed it do so and you obviously wouldn’t receive the pop up notification at the bottom right of the screen.
Safe Zone is designed for you to do your banking and shopping.
Which should be secure sites.
It isn’t designed to be used as your default browser. 
;D Yeah, I know but other people who use this computer use the SafeZone for banking and shopping and then can’t be bothered to switch to IE or Firefox after when surfing, does it still work with MBAM though?
Interesting question. My first thought is that you would be protected at some level, however not sure.
I don’t believe it can work with MBAM malicious websites function, as the SafeZone (including its custom browser) is isolated from the normal desktop.
The point at which MBAM malicious websites would get involved if you tried to connect to a malicious website using your normal browser. I say this as I believe MBAM isn’t acting like a firewall which would intercept connections outside of your normal browser.
Personally I feel that the MBAM malicious websites function is its worst aspect, as it doesn’t do what it says on the tin, only block malicious websites. It blocks much more than malicious websites, other categories unrelated to being malicious websites. Generally I turn that feature off, but a few version updates ago, doing that resulted in the tray icon changing to a grey icon.