I have been using ATEM for a few years, great stuff, no scalers on inputs so all input resolutions and frame-rates must match- it still gives you one input at a time (if you use it to feed a capture card).
The USB 3 capture built in to the old 2/me is not worth using and the ATEM television studio USB 2 is h264 encoded and cant be used for capture.- you will need another capture device
There is a an ATEM osc bridge that works with late but not latest firmware versions, the atem is a mixer and will not get you 3 simultaneous cameras, the tv studio model also does not have aux outputs so if you use it as mixer for your outputs you have no aux feed for your capture box.
https://github.com/danielbuechele/atemOSC
Your original question asked about 3 cameras into izzy- this does not help for simultaneous capture you though so it is unclear what you are after. If you only need one camera at a time then you have lots of options and dont need 3 inputs just some kind of switcher- as in the other thread knowing if you have to have smooth transitions between cameras with effects changes the requirements.
For simultaneous inputs the other thread has some info, but there is nothing that will really work for gen 1 thunderbolt, apart from a quad split device running to an HD capture input. Your USB 3 is the only option to keep an output free for the projector.
The blackmagic clean switch router is another solution that can help you.
Depending on what you see in your future for hardware you may be better of looking at other solutions as the cost of all these little bits will add up.
Some more info about your use case can help.
Fred