Digital Photo Pro is in fact rendering the RAW file. That's its purpose - to interpret and display data from Canon's RAW format. For the most part every camera manufacturer uses their own version of the RAW format, and their own raw converter (which is what DPP is).
There are definitely differences between raw converters when opening the same file. Mainly this is due in the way that each is programmed to interpret the raw data. Depending on who you ask one converter may be better than another. Some people will argue that DPP gives the best conversion and that would make sense since Canon knows their own file format better than anyone else. The most recent Adobe converter seems to do a really good job too. The various raw converters don't talk to each other either - so if you make some changes in one, then load the file in another the changes won't be there (this could be the issue you're having, keep reading...)
If you're seeing a noticeable difference when you export photos then I'd ask if you're actually "transferring" (DPP lingo) the file from DPP to the other program or if you're "opening" the RAW files with your Adobe software (Photoshop, Lightroom, etc...). If you're comfortable using DPP as your raw converter, make your adjustments there, then
transfer as a 16-bit TIF file. The TIF file should look identical to your RAW after you have made adjustments (TIF actually has more "room" for storing color information than Canon RAW currently does). (this could be the issue you're seeing, keep reading...)
If you're confident that you're doing everything above correctly and you're still ending up with funky colors in your jpeg it could be a color management issue. If your original RAW file is using a color space other than sRGB, say Adobe RGB for example, and you then save it to jpeg with a sRGB color space you're going to see differences - especially in the blues.
Lastly, when you save to jpeg you're now working with an 8-bit file. It has much less "room" for colors than a RAW file or TIF file, so you'll see some differences almost every time. If you want/need to use jpeg then you have to live with it. Otherwise keep the file in a TIF format to preserve the colors.
When you look at it in CDPP, you aren't seeing the RAW file, you're seeing it as if it was converted to a JPG by your camera.
That is wrong. DPP does not show the camera jpeg. It is a raw converter and renders an image from the raw data. Hence why your jpeg settings have no effect on the RAW files outputted by the camera.