My problem with using Safari is that even after I click on the "review match" button on my page of matches and review my match and then return to my page of matches, the one that I have just reviewed is still on the page as if I had not already reviewed it.
I tried to then use Firefox and when it began to get quirky I started using Chrome.
Now what I do is have Safari open to my own family tree while having my match's tree that I am reviewing open on Chrome. In this way I can have both trees visible on my screen simultaneously.