To log out of ProRemote and disconnect from ProPresenter you can simply close ProRemote. If you want to manually disconnect in order to change connections or ensure someone can't accidentally log into ProPresenter, you will need to go into the app's settings.
At the bottom of ProRemote, tap on the "More" button then tap on "Settings".
Scroll down in Settings until you see the "Logout & Disconnect" option. You can also change the Automatic Login option here as well.
(*The Instagram feature seen in the screenshot above is no longer available in ProPresenter and ProRemote due to Facebook no longer allowing third party applications, such as ProPresenter, to do queries and display user feeds. See the full statement here.)