There are different ways to think about this. Do you want to report what he said to you, or do you want to report what he promised to do? The first way of thinking leads you to say something similar to "He said he would do it when he was rich" and that leads to #2. On the other hand, if you want to tell us what he promised, you would say something similar to "He promised to do it when he is rich" and that leads to #1.

option 1 is correct but "he promised to do so when he becomes rich" is more typical.

I would say, "He promised to do so when he was rich." It is a slightly awkward sentence, but it works. You could also say, "He promised to do so when he became rich," or, "He promised he would do so when he became rich."