Please, enlighten me what is this growth on my new plumeria and how to treat it. I also took a clean cut of one of the growths.

They look like adventitious roots that are forming along the stem. Is the main stem near the soil still firm? I read somewhere once that a stem will start pushing out adventitious roots when the main root system has rotted. Hopefully someone more familiar with Frangipani (Plumeria rubra) will be along to offer advice.

@Vboy with Lin looks like roots. The stem might have sustained injuries and with moisture in the air that's why you are getting aerial roots similar to when you are air layering a plumeria cutting. I would not do anything on it especially around this time of the year when your plumeria is getting dormant.

In spring you can decide if you want to root the upper part cut let it callous and grow separately. Or you can leave it as is.

In the spring, bag root that area. When you have lots of roots in the bag, cut off below the bag. Let the cut callous like you would do a normal cutting. The plant will already have a good root system in the bag to support it. Once the bottom has calloused, then go ahead and remove the bag and repot.