There's a lot of confusion about "asynchronous MODE" and "using an asynchronous sample rate CONVERTER" (and the way we named the options in the DC-1 doesn't help the confusion).
With the original type of USB connection (properly referred to as "an isochronous USB connection"), the audio signal clocking is controlled by the computer. This type of connection has a lot of jitter, and is known for not sounding very good. Some low-cost DACs these days still use isochronous USB - but better ones do not. Virtually all good quality DACs these days instead use what's properly called "an asynchronous USB connection". In an asynchronous USB connection, the DAC clocks the signal instead of the computer. Because of this, the amount of jitter depends on how good the USB input clock on the DAC is - but even the poorest DACs do far better in this regard that a computer. Both our XDA-2, and our DC-1 have asynchronous USB connections. (Note that this affects ONLY the USB input since it describes ONLY the USB input circuitry.)
An asynchronous sample rate converter (ASRC) is a hardware device (although it can be done in software) which takes an input signal and re-clocks it. The ASRC takes in your original digital audio signal, and a new "clean" clock, and it puts out a new digital audio signal which is equivalent to the original signal, except that it is at the sample rate of the new clean clock. Most ASRCs use a single fixed-frequency clock for their "clean clock", and so convert the incoming signal (whatever sample rate it starts out as) to that fixed new sample rate; the purpose of the conversion is to eliminate jitter by re-clocking the signal to the clean clock; the rate conversion is actually "a side effect" of the process involved. This is the way the ASRC in our XDA-2 works. The ASRC in our DC-1 is a lot more sophisticated. The DC-1 actually detects the original sample rate, and then creates a new clean clock for the ASRC that matches that original rate. (So the DC-1 "converts" the signal to the same sample rate as it started out - but using a new and cleaner clock. This therefore avoids any possible change in the way the audio sounds that might occur BECAUSE you were changing the sample rate, but still removes the jitter.
The USB input on the DC-1 is ALWAYS in asynchonous USB mode. When you select "asynchronous mode" in the menu, you are selecting "ASRC enabled"; when you select "synchronous mode", you are DISABLING the ASRC. While the terminology we used is technically correct AS REFERS TO THE OPERATION OF THE DAC ITSELF, it does NOT refer to the USB input mode, and so can be somewhat confusing. When you enable the ASRC in the XDA-2 or the DC-1, it is applied to ALL inputs; the ASRC re-clocks and so removes the jitter from ALL INPUTS including USB, Coax, Toslink, and AES/EBU. (Since the asynchronous USB input should be quite free of jitter anyway, you shouldn't expect enabling the ASRC to make much if any difference in sound when you're using the USB input, but you can turn it on (or leave it turned on) if you like - and it shouldn't hurt anything.)
Without getting into a long discussion about whether changing the sample rate will be audible, using the ASRC should NOT introduce hum, noise, or hiss into the digital audio stream. We have received a few reports of DC-1 units which seem excessively sensitive to noise only when the ASRC is enabled.... or that actually produce hum or buzz only when the ASRC is enabled. This is NOT due to the action of the ASRC itself, but rather due to the fact that the circuit paths inside the DC-1 change when you enable the ASRC, which affects the grounding of the analog audio circuitry. If your DC-1 makes hum or buzz when the ASRC is enabled, and this changes when you select different sample rates on the computer, then either your DC-1 itself is faulty (and so digital noise is bleeding through into the analog circuitry internally), or your DC-1 is faulty in a different way, and so is being unusually sensitive to ground or power supply noise from your computer (and so you are "hearing" the difference in noise produced by your computer at different sample rates THROUGH the DC-1.)
This is not normal operation for a DC-1, and you should NOT hear hum or noise on the DC-1 when the ASRC is engaged (not at ANY sample rate).