Translation:You will do the dishes after you arrive home.
I think most people would just say "arrive home," but it's not accepted. Reporting.
You'll do the dishes after you arrived home is accepted, but with a Typo? I don't see the Typo.
"arrived" has an extra "d" compared to "arrive".
I don't think you can use the simple past here for an event in the future, so it has to be either simple present or present perfect ("after you have arrived").