CD to DAC to DAT to DAC?

So I receive my Panasonic SV-3800 DAT deck yesterday...

I connect my turntable to the analog input (obviously) and connect my CD player to the digital input (TOSLINK).

I then take the coax out on the DAT deck to my DAC (and then out to the amp over RCA).

For some reason the DAT deck acts like the CD player isn't there. Do I need to run it into the DAC, then out via coax back to the DAT, and then back out to the DAC (and then into the amp)?

This doesn't seem right to me, but I'm just a bit baffled - I mean, does the signal from the CD player need to be processed prior to hitting the DAT?

Thanks,
Mark