Hey, I'm no expert but I have been colouring my hair for years. I would say you can use your non-colour-safe conditioner but it might just strip your colour a little faster than would a colour-safe one; sometimes the colour-safe ones actually deposit a little bit of colour onto the hair to help maintain it. Reds tend to fade really quickly unless you have been dying your hair red for a long time. Also, you could have seen the colour run out because you used a demi; demis fade out gradually faster than a permanent would. Maybe a colourist could chip in?
pw: curlie