I recently tried to add a subdomain CNAME, e.g. 'foo.mywebsite.com', but it did not work initially because I was missing the trailing '.' that is required. I had to contact DigitalOcean support, which delayed things a few hours, but they informed me that one has to either include the trailing period (.) ('foo.mywebsite.com.') or else only include the subdomain ('foo'), in order to have the desired effect.
My suggestion: the DNS control panel should warn users whenever it looks like they are creating a CNAME for a subdomain but missing the trailing period, so they can avoid this confusion. I'm imagining a little warning box saying something such as, "Hey, it looks like you're adding a a CNAME for a subdomain. Did you mean to include a period (.) at the end?".