HDMI is one monitor to one computer point to point. Display port is one monitor to one computer point to point. The thunderbolt port has two channels and there may be a way to connect two monitors by daisy chaining (in theory), but I dunno if anyone does that. Currently a Mac only supports one monitor per thunderbolt port. If your MacBook Pro is like mine, it has two thunderbolt ports, so you can drive two displays (over separate cables) if you want (but be ready for lots of heat). There are DisplayLink USB-graphics adapters that will connect multiple displays to a single USB cable to the computer USB port.
My monitor has display port, DVI, and HDMI interfaces. I connect my rMPB to the display port, my MacPro to the DVI, and my netbook to the HDMI. I use the switches on the monitor to select what to view. The computers detect when the monitor is connected, well the netbook kinda sorta.... but thats a windose thing.
I have just the one cable to disconnect from the portables when I want to go portable. In fact the LG monitor can be configured for split screen, where one computer drives one half and the other computer drives the other half. There is a PIP thing too, but I haven't played with that.
Display port or DVI will give you much better computer PQ than HDMI. HDMI is fine for movies and if thats the only thing you have you make do with it.
Anyway, the device you referenced sends the identical video to both monitors, you pick the input. Your Mac will not know that there are two monitors out there, it just thinks there is one. In other words, you will see the same picture on both monitors regardless.
You can't connect monitors to the device inputs... the switch device inputs can only be connected to sources... like your computers. Computers connect to the switch device input, monitors connect to the switch device outputs. The same signal will appear on each output of the switch device you referenced.Big bucks will get you something more elegant.
I don't know of a device like you are looking for, but there are KVMs that can switch DVI.