If your app is still showing your old account details or an incorrect £0 balance on the morning of your switch, it's likely your app just needs a chance to catch up. Here's what you should do:
Force-close the Countingup app by swiping it away completely from your phone's task manager/app switcher.
Reopen the app.
Note: Logging out and logging back in will not clear the display cache; you must completely close and reopen the app.