The cause of the problem was not 'immediately' clear. [=is was not known right away]
They live in the house 'immediately' [='directly'] behind this one.
We need to leave 'immediately'. [='at once', 'right away']
(..) Does it mean anything to either of you? No. Could l have your attention, please? Because of recent events, these new rules will be put into effect immediately: ''All students will return to their house common rooms by every evening. All students will be escorted to each lesson by a teacher. (..)2002 Harry Potter and the Chamber of Secrets
(..) l'll kill you. -l'll kill you! -Argus! Argus, l. . . . Everyone will proceed to their dormitories immediately. Everyone except. . . . . .you three. Ravenclaws, follow me. She's not dead, Argus. She has been Petrified. (..)2002 Harry Potter and the Chamber of Secrets