Like others have stated, it looks like it's just trying to send out new foliage. I doubt a plumeria will bloom indoors. A warm sunny window with afternoon sun is great, but it's no equivalent to a warm sunny location outdoors with sun shining on it throughout most of the day.

I just recently repotted my 'Hilo Beauty,' and it's a single stem that finally started branching, and it's getting almost as tall as I am. All I did was shove a fiberglass stake into its pot and secured it with some of that flexible green planting tape, so that it doesn't pinch the trunk as it gets thicker.

And as for worrying about bugs, I wouldn't. Sure there'll be the occasional one here or there, but it's not like our potted plants are a magnet for pests. That is more of an issue for plants grown indoors, where insects have limited options on where to go. They're not going to find much food or shelter inside of our homes, other than any potted plants that we might have sitting around for them to go to. I couldn't even begin to guess how many potted plants I have, but I can say for certain that pests are rarely something that I ever have to deal with.

I used to try and keep many plants indoors all of the time, where I could control every aspect of their environment (or so I believed), but that makes plantkeeping more of a chore, rather than a hobby. But after many years of killing off plant after plant, I no longer do that anymore. Now all of my plants go outdoors once the weather warms up. No exceptions. Some stay on my shaded porches with little to no direct sunlight, while others get placed in locations where they get sunlight all day long. All I do is keep them watered and give them the occasional dose of diluted fertilizers when needed.