I don't really think Tarev meant to say "pitch it", which means "throw it away". IF you have soft, mushy stem tissue develop on the CUT END, just cut that stem back above the soft area. The tissue should be white and ooze "sap". If you still see brown/black tissue, just cut back some more until you come to firm, white tissue. If the other end, that end with the small, just-forming leaves, rots - well, the plant is toast. It is time for the garbage-toss!
DON'T water your unrooted plumeria at all. Just keep it/them warm (50 F or above is fine). You can keep it/them on a shelf, on the floor, wherever. It doesn't matter whether there is a lot of light or little light. Plumeria are not growing during their dormant time anyway. If you have medium ready to root that/those plumeria (such as a pail of coarse perlite) you can go ahead and stick your plumeria 3-4" deep in that. It is not rooting time yet, but it won't hurt to store it/them that way. I have dozens of cuttings stored just like that, a dozen per coarse perlite-filled pails. They have been that way for two months and have not started growing any leaves. They will begin to root in the spring but other than misting the terminal leaves, I won't begin to water and won't put them in a semi-shaded location outside until I see nice leaf growth. I will only lightly water even then. Of course, they won't go outside until my low temperature stays at or above 50 F.
It does not matter whether you have a red, white, yellow, or rainbow Plumeria. Just treat them all the same. Keep in mind that red plumeria are much more difficult and take much longer to root than the others. The redder the flower, the longer and harder the rooting.
