Actually, I have a pretty good idea what he did.
Your Eclipse was originally equipped with a stock Infinity sound system, which includes a factory amplifier located under the passenger seat. There's a special harness available to install a new head unit and keep the factory amp working. This harness uses the deck's RCA outputs instead of the speaker outputs. Your head unit has four speaker outputs, but only one pair of RCA outputs; which is why everything is running from the rear channels of the head unit.
When you're installing new audio equipment in one of these cars, you have the choice to keep the factory amp working, or to bypass it. Generally, when I'm installing new speakers along with the new deck, I'm always going to bypass the amp. If someone's keeping the stock speakers, then it's best to keep the stock amp as well. Bypassing the amp means connecting the new speakers directly to the head unit's speaker outputs, instead of running them through the amplifier. Your installer should have bypassed.
The easiest way to fix the problem is to purchase a Metra 70-7002 amplifier bypass harness. With this, you can unplug the factory amp, connect the plug to the harness, and run the wires up to the head unit location to connect to your new deck's speaker outputs.
The only downside to bypassing the amplifier is that you'll lose the factory tweeters and center dash speaker.