There is a couple of possible reasons I can think of.
Over stirring the mixture could be breaking the rice down releasing more of the starches which will be making the sauce thicker and sticking the rice into clumps.
Over cooked rice again making the rice overly sticky.
Like you've mentioned, lack of liquid. If the sauce is getting far too thick the starches will be more concentrated again sticking the grains together.
If the sauce is thick then certainly adding more water should help loosen it up a bit. Soaking the rice in cold water for half an hour before and then rinsing a few times will help get rid of some excess starch.
Also a possible factor is your choice of rice type. Some are more "sticky" than others.
Without tasting it myself it's hard to give a 100% reason but hopefully you will get a better result by paying attention to all the above.
If after all the above methods one last ditched effort might be as follow. 12 years ago when I was just starting out in my first kitchen I remember my head chef telling me "when you pour you're rice into boiling water, you must make sure they all fall freely and hit the water individually". Now I've remembered this ever since and thought about it every time I've cooked rice since, I've never done it though and can see NO reason why it would work or make any difference.
It's also worth noting I've never used a rice cooker in my life, not even sure what they are or do...