Hi,
Love the program but this has been an omission for a while now, the cache is cleaned from Chromium, but not the browsing history. This really should be taken care of by default if Chromium is selected in apps.
I have had to add the following manually in Custom Files and Folders:
~/Library/Application Support/Chromium/Default
Hope this is of use, and hope the developers fix this issue with the next release!
G