Have you checked to make sure the colour correction profile is correctly installed in Corel and also double check your settings in the Epson driver. Assuming this are fine try pressing your mugs for an extra 20-30 seconds as the length of time you press for (and the higher the temperature in your mug press) will darken the image reproduction on to your substrate (mugs, ceramics, textiles etc).
Red is a hard colour to produce on dye sub migs in my experience. It is a bit trial and error but do as mbroad suggested. Remember though, that you will reach a limit where the colour will start to bleed so keep a look out for that.
Please note:
This action will also remove this member from your connections and send a report to the site admin.
Please allow a few minutes for this process to complete.