Audio compensation is usually handled by the DAW software automatically. Check Preferences in Audition to make sure it is not turned off. Reaper and Audition should work identically as long as the computer is fast enough and has plenty of RAM. Audition is heavier software and uses more resources and that could be the problem.
Alternatively, try reducing the latency with the slider in the preferences you show in your Dropbox png's.
Try another USB port especially if you are using other devices (hard drives) via USB, or remove the other USB devices and test.
Check for newer drivers for your audio interface and keep the older versions. You never know when you will need the older version when the newer drivers fail.
Do you have the 32 bit version available of Audition, try it.
Last resort would be to try using another audio interface, even a cheap one for comparison.