IIRC the powering on by WiiMote is handled by the BT chipset which stays powered in all power states and in the normal standby mode wakes Starlet with dedicated GPIO line. Also, while the WiiMote is more or less an compliant BT HID peripheral with custom report protocol, the power button is handled in different somewhat weird proprietary way.
Another thing is that there are two different standby modes for wii once first booted (can be configured in settings), in one the Starlet is completely powered down (red LED) and in the other it stays on and runs scheduled tasks (orange LED). In early hardware revisions the fan is stopped in the orange mode, while in the later revisions it is temperature controlled (the first revisions will overheat and degrade/destroy the GPU if left in this standby mode for too long).
Another thing is that there are two different standby modes for wii once first booted (can be configured in settings), in one the Starlet is completely powered down (red LED) and in the other it stays on and runs scheduled tasks (orange LED). In early hardware revisions the fan is stopped in the orange mode, while in the later revisions it is temperature controlled (the first revisions will overheat and degrade/destroy the GPU if left in this standby mode for too long).