Perth T3/T4 is a single terminal. Your check-in desk was just located in the area designated "T4".
The weird security setup is because the "international" section of T3/T4 is inside the domestic airside area. The first security screening is to domestic standards i.e. no liquid restrictions and anybody can enter even if you are not flying.
Unless I am mistaken, you could have gone airside at a checkpoint in the area designated as "T4" as it's connected to the gates in the area called "T3".
The second security screening is to international standards i.e. ticketed passengers only and liquids in 100ml containers. I think the second security is after immigration, so the ABF can stop clueless people going through when they didn't mean to. (I've only been through there once.)
Thanks, we just followed the advice of the check in agent for the route to follow, but the two standards explain it all, if not the most efficient design for passenger flow!