Three questions here.
This is a personal opinion: Adobe likes o complicate things.
Yes, that is not RGB or RYB models. It is not Lab. When you have a model that is not standardized, and you do not provide any explanation on why that "new" model is "better" on anyway, it is a bit useless. If you like the results, it's ok to use it, but again, IMHO, do not use that specific tool to understand color theory.
There is a chance that the color wheel tries to simulate RGB values for CMYK colors or something like that. The perceptual value of Cyan on an RGB monitor does not correspond to the pigments currently used in the different printing industry. But again, if they do not make a minimal effort to explain the logic behind that wheel, there is no use for it, except just a tool.
Take a look at these other questions.
Is there a name/formulae for the hue-circle scaling Adobe is using with "Kuler"
Is there a standard for color wheels?
It is hard to generalize. A lot of people use an RYB model, especially, IMHO for children and in art schools, when the main tool is physical paint.
But remember that this is not an "exact" model. The tones are used in a general way, which is the yellow yellow? and which tone is the correct blue?
In painting, you use different tones of yellows, blues, reds. You rarely try to use only primary colors.
When printing technology is taught, you have to use the CMY-RGB model.
On the current digital photography world, the RGB model is normally used, and a bit of Lab.
An online tool to do what?
You are probably referring to websites to make palettes or color schemes.
There are some other websites, making a search here on stack exchange you can find some lists.
The RGB-CMYK color wheel is pretty standard, not on online websites but in programs themselves.
But color is a bit subjective, it is a perception thing, not only a "mechanical" construct. This is why we have different models. RYB, RGB-CMYK, HSB, HSL, Lab, Munsell.