You're right. Bacteria is attracted to oil which is one reason oil pulling works. And you definitely HAVE to not only spit out the oil when you're done but also thoroughly rinse your mouth afterwards.
That product isn't an oil at all and appears to be a clay with some additives. I'll swish around clay often when I have some kind of mouth infection or tooth pain. Between that and oil pulling with a few drops of oregano oil, any kind of mouth infection you can imagine is taken out. Bentonite clay is powerful stuff.
But keep in mind this is a completely different thing than oil pulling with different benefits and results. If the product is mostly clay (which I'm sure it is) it actually IS ok to swallow it (as long as it's quality food grade clay). The great thing about clay is that it binds with germs, toxins, metals, etc and doesn't release them back into your system. It gets eliminated with the toxins still bound, and when it comes out it looks a lot like it did going in.
Clay is good for absorbing infections etc but won't touch what oil pulling can do for general oral health.