[subject] + [verb] + 了 + [object] + 就 + [verb phrase]
[verb] + 了 + [object] + 再 + [verb phrase]
了 after the first verb says that action is finished before the second one starts. 就 or 再 before the second verb links them: "after X, Y". This 了 marks completion, not past time, so the frame works just as well for tomorrow.
就 says Y follows straight after X, with no delay, and works for past, future and habits. 再 says don't do Y until X is done; it looks ahead, to plans and requests.
When the second action is in the past, 再 doesn't fit. Use 就, or 才 if it happened later than expected.
了 sits right after the first verb, before its object: 下了课, 吃了饭. With a complement, it follows that: 做完了作业.
先…再 sets out two steps in order without stressing that the first is done; 一…就 stresses that the second follows instantly.