Steinbergusers.com: Tracks bleeding over

I just set up Cubase Studio 4 on an XP desktop last night, running my band through our various amps into a Peavey PV20 mixer and out through the USB cable into Cubase Studio 4.
I am new to Cubase products, this being my first one. In fact we are new to recording with software, period!

Last night the band put down some tracks to test CS4. One of the things we noticed is that even though each instrument was being recorded on its own track, when we played the tracks back through our monitors we could see in the Cubase Studio 4 mixer that the instruments were bleeding over onto other tracks.
In other words, I could turn the lead guitar track all the way down in CS4 and yet the instrument could still be heard through the monitors and we could see it with the output meters in the CS4 mixer.

Is that normal or have I left some necessary task undone in the setup?
Is a USB cable incapable of sending the signals/data in such a way that it keeps the tracks separate from one another? Is the software simply not able to contain the instruments to their individual tracks?

We are home recording virgins. Total noobs. Any help would be greatly appreciated.

Thanks in advance!