It's kind of a tradition = I'm using a manner of speaking when I say that it's a tradition. [In fact it may have happened only once previously.]
It's a kind of tradition = It is (unarguably) a kind of tradition.
But I don't buy this distinction. 'Kind of' is, as you say, 'a softener', and people just drop it into the sentence in either position. (In an exam, though, If I were you I'd follow the dictionary's preference!)