How Do Wall Kicks Work In Tetris Friends?
Solution 1:
With SRS, all pieces follow the same kick table except for the I-piece.
What you describe happening is exactly how SRS is supposed to work. In either case, rotating left or right will have the same effect here. Going from the original state (state North) and rotating right will first try no kicks. The piece overlaps and tries the next kick offset, -2, 0, which shifts the piece left two columns.
If you try to rotate left, the natural rotation is tried, fails, and the next kick, -1, 0, is tried and works, the piece moves left once. Because the natural left rotation moves the piece left already, it ends up in the same position as a right rotation.
This while not important to your question does bring up a left bias in the I-piece rotation, that isn't seen with the other pieces.
The reason these rotations were chosen is kind of a side effect of how SRS works. With SRS, all rotations are reversible. This means when you rotate and a piece kicks, you can always rotate the other direction to get yourself out. These kicks are just meant for the piece to be able to rotate off of a wall, but the side effect is the reverse (what your example is) has a weird behavior.