V + 자마자 is used to say 'as soon as you V' or 'immediately after V-ing':
어휘
이주하다 -- to emigrate (to...)
끝내다 -- to finish doing sth (vtr)
낮잠을 자다 -- to take a nap
조용하다 -- to be quiet
V + 은/는 대로 has two different meanings when added to verbs.
은/는 대로 can be used with a verb to say 'as soon as you V'. Note that both actions have not yet occurred, so it is only used in the present tense. It is identical to 자마자:
도착하는 대로 연락하세요.
Please contact me as soon as you arrive.
새 상품이 출시되는 대로 매진될 것이라고 생각해요.
I think as soon as the new product is released it will sell out.
친구가 돌아오는 대로 편의점에 갈 거예요.
I'll go to the shop as soon as my friend gets back.
답안지를 받는 대로 시작하세요.
Please start as soon as you get the answer sheet.
비행기를 이륙하는 대로 아기는 울기 시작했어요.
As soon as the plane took off the child started to cry.
은/는 대로 can also indicate that you do as someone else has done:
메시지를 들은 대로 썼어요.
I wrote the message down just as (exactly as) I heard it.
내가 하는 대로 하지 말고 내가 말하는 대로 해라.
Do as I say not as I do.
어머니가 하는 대로 저도 김치를 만들었어요.
I made the kimchi just as my mother does.
친구가 말하는 대로 했는데 저는 문제를 못 풀었어요.
I did as my friend told me, but it didn't solve the problem.
제가 조언한 대로 한 거... 괜찮아요?
I followed your advice... is everything OK?