Hybrid teas are usually grafted onto a rootstock to provide extra vigor. The necessity for the extra vigor varies by location and variety. Aloha *should* be OK own-root.

The variety of rootstock used is selected by the grower.

If you root cuttings from the branches, you are getting Aloha. Sometimes roses change over time, so any changes that have happened are still there.

Pretty much what mad_gallica said, except, the preferred method of propagation in the US for the majority of the past century has been budding. Some varieties require the extra vigor artificial roots provide. Mostly, it's been to push larger, more mature plants of a variety out the door faster. Aloha has been offered own root long enough to have a proven track record of its own root performance. You MIGHT wish to grow it on in a pot until it's more mature before setting it out in the ground. Young plants are "infants". Treat them as such and you should be fine.

If you take cuttings of the Aloha, you will pretty much get what the most recent flowers you've seen have been. If there are root stock suckers and you accidentally take some of them for cuttings, you'll have infant root stock plants. As belle_gallica indicated, any possible mutations which may have occurred within the material you've selected as cuttings will likely be reproduced in your own root plants. If you've not noticed any variations from the normal Aloha flowers, foliage or growth habit, don't expect the new own roots to differ from them as they probably won't.

If the original plant came from a long established American source (J&P, Week's, or older US major producer) since World War II, your chances are greatest the rose is budded on Dr. Huey. From other sources, it may be on multiflora. Different producers have selected different stocks depending upon where the majority of their plants are destined to be sold and where they produce them. Kim

Thank you both for your replies. They were very thorough.
I do have a couple of baby plants that I started from cuttings two years ago. Their flowers are pink, but don't have the intense (and varied) colors of the adult plant. I assume this is because they are too young to put out the really gorgeous and large flowers of the adult. Time will tell. I'll also try budding and compare if I have success with that.