The image labeled nomagnet show two flat lines which I thought was weird because shouldn't the clock always be on, or is there an on-board feature of the MLX90333 that only turns the clock on when a magnet is near?
You should definitely see a clock signal at least when the CS line is low. May I ask you to connect the scope to that line in addition to the clock line and trigger on the falling edge of the CS line?
As the clock is handled by the Arduino the MLX90333 cannot switch that signal on and off.
None of the signals I see on the pictures is from a clear SPI signal. On what event were you triggering?