Thunderbold to HDMI ---> HDMI Switch ---> Saeco projector = No Video
There are no real differences between HDMI 1.3 and 1.3b so I would blame either the switch (most likely), the cables (do you have the correct ones for each device), or even the configuration settings on each machine.


If you plug each one into the projector individually do they work? If so, it is your switch that is at fault.
If not, try replacing the cables and connect each one to the projector - does this solve the problem? If so, the cables were the problem.
If not, check your configuration settings for the display on each machine.