First of, you might want to clarify the terms in your question. In the first paragraph it seems that a "piece" is what others might call a "tile"; i.e., each tetromino is composed of four "pieces" or "tiles". But then at the end of the paragraph you call it a "block". And then, in the second paragraph it seems that "piece" is synonymous with "tetromino": "the piece has landed", "move his piece". So in your question, what do you mean? Perhaps "Which tile should the tetromino rotate around?"
If that is indeed your question, the answer is it's implementation-defined. If you try different versions of the game, you may see that in some, the "I" piece will wobble left-right or up-down as you put it through two rotations (the rotation tile is fixed on the tetromino), and in others it will not (the rotation toggles between the two center tiles such that a CW rotation will have the same effect as a CCW rotation). The "S" and "Z" pieces will similarly either wobble or not. If they don't wobble, though, you might find that a piece will be able to rotate when it's against the left wall but not if it's against the right, even though the situations should be symmetrical. And the square piece, if you leave it with a fixed rotation tile, will rotate around a corner when in all likelihood you want it to (appear to) not rotate at all. I've never seen an implementation that doesn't at least take care of that!