Log in to your CarePro web app, at thediary.com, with your username and password. (The login for your CarePro web account is identical to the login for your CarePro iOS account.) From your CarePro web account, to log out, click on your account image circle at top left.
You will then be able to click on the words "log out", which will log you out immediately. (Note that there is no prompt asking you if you are sure you want to log out.)