I could be wrong, but I'm not sure that's what Tarski was talking about. I think this quote has more to do with getting at the nature of the relationship between a proposition (snow is white) and its representation (the string "snow is white"). Beliefs are somewhat irrelevant, or at least thinking about them goes well beyond the point made by the Tarski quote.

The relationship between a proposition and its representation is analogous to the relationship between reality and beliefs about reality. It's identifying truth as correspondence.