After a second thought, it’s good - since even after a full scan without real time installations of apks are not tested, thus one remains without a “concurrent” full scan.
Regardless of how I invoke full scan (via fix it / start here or just scan), it always show full scan not made and issue needs to be fixed (“Fix it” via notifications).
I’m failing to get any indication whether “safe browsing” is available / active regardless of browser (ROM - I’m using S3 - lte / I9305 with 4.4.4 original ROM / Firefox / Chrome).