Hello; I have seven tiger barbs that have grown to maturity in one of my tanks over four + years. Some have a very red snout. I suspect these are males and from time to time I have observed what appears to me to be a way to establish a pecking order (dominance) that is similar to what you describe. The male that comes out on top looks to have the redder nose that the others with a red nose. Much of the time they all get along without any squabbles. Some many months ago the when there were ten tigers the biggest with a red nose died. I noticed that the pecking order was disrupted and after a time another slightly smaller red nose apparently came out on top with the reddest coloration of its snout.
I have also observed some chasing and what could be described as dancing between what I take to be the males and the females. This often results in some very vigorous chasing of what I think are females thru the heavily planted part of the tank. I suspect this is mating behavior and that eggs are likely shed. No fry result as it is a community tank.
What you have seen could be a mix of both behaviors.
