Is TDI shifted on move from SHIFT-IR to EXIT2-IR in JTAG?
You are correct. Data is shifted if the state at the rising edge of TCK is SHIFT-IR, and the next state is entered after that.

Thus, the bit at the transition from CAPTURE-IR to SHIFT-IR is not shifted, and the bit at the transition from SHIFT-IR to EXIT1-IR is.

Thus, the protocol decoder is broken.