Dipping your brush into water isn't going to do anything other than get your brush wet. To actually clean a brush, you need physical agitation, and I don't mean "swish it around in the water jar a few times" agitation, but "mash it back and forth against your other hand while holding it under running water" agitation. Use some paint brush soap (or plain old hand soap) and really work up a lather. Rinse and repeat until the lather bears no trace of the pigment you were using, then rinse thoroughly.
If this sounds like too much work when all you want to do is switch pigments, there are two things that will help. One, don't put so much paint on your brush: put the paint on just the tip, not the whole thing. Of course, that's not a terribly effective way to paint a large area such as a background, which brings me to: Two, get more brushes. Basically, use one brush per color, or at least per color family. If you're switching between, say, vermilion and cadmium red, you can get away with just swishing the brush around in the water jar and wiping on a paper towel. You still need to do the thorough washing as soon as possible after you're done, though, since acrylic paint can dry on a brush even if it's sitting in water (plus, sitting in water is itself a bad thing for a brush).