"EXT" means extender, not external.
IR control signals are serial-packets of pulses received from your remote. Becus they are serial, they only need 2 wires to deliver the pulses. Extender modules relay this signal, sometimes by radio from other rooms to your unit, so it is an INPUT on the HDMI switcher. So you would plug your IR-rcvr unit into it.
Any IR repeater system will work. They all have a 2-pole 1/8" plug that plugs into whatever amp or switcher your want to control. My favorite IR system was Radio Shacks Pyramid. The pyramid shaped modules were dark red plastiic w/wall wart supplies, but were battery capable.
You set up the sender unit from where you control things; master BR or media room, and plug the rcvr into the amp/switcher. It would repeat any IR signal aimed at it.