Communicating yes, but while the LED may glow, you can't operate 12 V relays - as they clearly are - on 5 V.
Well, you clearly do not understand them, because they can be selected to operate either active HIGH or active LOW- that is why it is written on the module!
It certainly is not, but blessedly, he was not attempting to do so. Using "Vin" or the "barrel jack" is always a bad idea for a serious project. 
You can use this relay module. The proper way to do it is to connect "DC +" and "DC -" to your respective 12 V supply terminals by a twin cable. Then remove the two jumpers and connect one or both "com" pins - depending on whether you want to use both relays - to either your Arduino ground if you wish to have the relay(s) active on HIGH, or to "5V" if you want them active on LOW.
Connect the respective "IN" terminal to your Arduino, keeping this wire together with the one connecting the "com" pin to the Arduino ground or "5V".