Dither fish definition is actually substantially broader than that. The basis for/of a dither fish or group of dither fish is to distrack some other fish or group of fish.
It may be, as already mentioned, to distract a breeding pair from a third conspecific in the same tank, or simply to give the male an outlet to guard against so his inate fry defense aggression will not turn against his partner.
Or, it may be to provide a shy retiring fish with the signal that "the coast is clear, no predators are arond" - another common use of dithers - where a single specimen fish may be spooked and not swim/feed normally as no other fish can be seen in the tank.
And even, although not usually intended this way, adding fish to a too-small school of the mentioned Tiger Barbs would provide conspecific dithers, so the hirarchy of the school fully used up the aggression of the Tiger Barbs, leaving nothing left over to be shown against non-Tiger Barb tank mates.