I don’t use Scratch Pro, so can’t help you with that particular thing. It does sound really odd you’d need 4-channel mixer to mix between TC and vinyl though.
The general routing is this:
1) TT output (depending on TT this is either Phono or Line level output, usually RCA)
2) Digital mixer with built-in DVS-ready sound card, controller with built-in DVS-ready sound card or sound card with minimum two stereo phono in (or line in if your TT outputs that).
3) For DVS the sound of the TC goes to the control bits in the software. You switch between analogue and DVS in the software, depending on the setting the sound is sent to the sound card (either built-in in mixer/controller or external sound card). That sound will either be an MP3 manipulated by DVS or the actual analogue sound routed through the software and right back out.
With an external sound card I know there is an option on some to switch between DVS and thru on the sound card (should your software not support that option). It effectively routes the phono input after RIAA-correction and gain amplification to the line outputs from the sound card.
In all these cases an additional two channels should not be needed.