Your understanding is correct. Please see more examples below. 1) ~자마다: as soon as; no sooner ‥ than ‥; hardly[scarcely] ‥ when[before] ‥; immediately after; 그녀는 도착하자마자 병에 걸렸다. She had no sooner arrived than she fell sick. 그는 대학을 졸업하자마자 사업을 했다. Immediately after graduating from the university, he went into business. 2) ~는 대로: as soon as; at one's earliest convenience. 서울에 도착하는 대로 전화를 하시오 Call me as soon as you arrive at Seoul. 기회가 닿는 대로 찾아 뵙겠습니다 I will call on you at the first[earliest] opportunity. 3) 후, 후에, 후에는 All these words mean "after, later or since". 그 후에 그는 어떻게 하였습니까? What did he do after that? 그는 물을 마신 후에 말을 하기 시작했다 After drinking some water, he began to speak. 그 후로는 그를 만나지 못했다. I haven´t seen him since then.

1) Actually the two overlap a lot in the meaning, but "A...ㄴ 대로,...B" is usually used when B is closely related to A. On the other hand, B has got nothing to do with A in the pattern, "A...자마자, B..." 집에 도착하자마자, ....(lots of things(even you don't know) will happen) 집에 도착하는 대로, ...(you know exactly what you should do or say, or what will happen) 2) "후" is a noun, and "에" makes nouns into adverbs like, 아침 = morning, 아침에 = in the morning, 오늘 아침에 = this morning 후 ☞ noun, 후에 ☞ adverb "는" is just used to emphasize "후에" \^o^/