Cuttings do not need ANY water after the initial watering until AFTER the roots have formed. With no roots the cuttings has no way to take up the water to the leaves. Cuttings also need bottom heat to form roots. Watering without roots will certinally hasten rot. As far as the discoloration of the leaves, I have no idea what could be causing it. One of our resident experts will surely come in soon.
Andi

Thanks. The package said to water once a week after planted so that is what I have been doing. How do I know when I have roots? When I planted them they didn't have any leaves at all and the first leaves started forming within three weeks. They have been in the pots for almost three months now.

You can VERY CAREFULLY move the soil aside along the bottom of the cutting to see if you have roots. You can give a slight tug upwards and see if you feel resistance. resistance means roots. If you move the soil aside you can check for rot at the same time. The soil will have to be scooched (technical plumie term) aside to the base of the cutting.

In 3 months it should have roots but there are some that take longer.

Plumeria cuttings have enough stored energy to root. They use this energy to also form leaves. This is why many people cut the leaves off non-rooted cuttings. This way the cutting will direct its energy to forming roots instead of leaves.
Andi

Can you wipe any of the black stuff off of the leaves? Some very teeny tiny insects leave a sticky substance behins and a mold like stuff can grow on it.

No, the black stuff doesn't come off. It is all the way through the leaf. It is hard to see in the picture, but where the black spot is it is curlled up. This particular tree was the one I called "the good one" because it sprouted its leaves quickly and had about five before the other one even showed signs of having a leaf. I'll see if I can check for roots today.

I'm not sure what that discoloration is from. Is the entire stem firm? Andi gave you good advice, NO WATER! Once you have several good sized leaves you can be fairly confident that roots have developed, not always but it's a good rule of thumb. What zone are you in? If you aren't in 9 or warmer you might want to consider a seed mat because nighttime temps are starting to drop. I'd cut off the affected foliage (leave the leaf stem attached to the trunk). I wouldn't go digging around for roots. If there are any checking for them might very well cause damage. They are very brittle. Good luck.
Karyn

Thanks. I don't know what zone I am in, but I am in the deep south. The plants are indoors so they are at a constant temperature right now.

The stem is firm, the leaf is nearly all black now and the stem still has the reddish brown streak going up it.