All signal processing takes place within the computer, and this is for a number of reasons. First and foremost, today's computers are powerful enough to handle even big mix sessions, so adding a DSP chip is unnecessary. It would also have added to the cost and it would have meant that the user was forced to always have the hardware connected. Furthermore, Console 1 could not have been solely powered by the computer's USB bus.
Console 1 does not require any more CPU power than you'd expect from any other Softube plug-in, and we're well known for making plug-ins with a low CPU usage (with TSAR-1 Reverb and Modular as possible exceptions). When you first add the Console 1 plug-in to a channel, all its sections are bypassed by default, and if you keep it like that, the CPU usage is barely measurable. But you still get pan, input level and output volume for that channel (as well as Solo and Mute), so we recommend that you create a mix template with the Console 1 plug-in inserted on all channels to get complete control of your mix from the Console 1 hardware.