Not sure of why minority races always seem to outpace by an extremely wide margin the founding race of an empire, but here's a very simple counter I thought might at least make sense.
Rather than the current system that seems to spawn other species almost 90% of the time why not go with a simple 1-1-1-1-1 system. Order of spawning would be determined by dominance of the races involved with the largest numbered species going first followed by the next until the newest arrivals get their population expanded. In this example I am suggesting that there are five races on a single planet. Each race gets one new pop every five pops that spawn with any new race migrating to that world simply getting placed at the back of the pack and adding a new 1 to the rotation. That way the sixth pop spawned should be the first or dominant species on the planet if there were five races in total.
Another thought is that on any colony ship if you have the expansion perk unlocked that gives you a second pop when the colony finishes it's initial development that initial colony group is only the race selected for the ship when building it. That way at least at first there's a good chance that the planet primarily populates for a time with the race selected rather than everybody else in the galaxy with a migration treaty with your empire.
Rather than the current system that seems to spawn other species almost 90% of the time why not go with a simple 1-1-1-1-1 system. Order of spawning would be determined by dominance of the races involved with the largest numbered species going first followed by the next until the newest arrivals get their population expanded. In this example I am suggesting that there are five races on a single planet. Each race gets one new pop every five pops that spawn with any new race migrating to that world simply getting placed at the back of the pack and adding a new 1 to the rotation. That way the sixth pop spawned should be the first or dominant species on the planet if there were five races in total.
Another thought is that on any colony ship if you have the expansion perk unlocked that gives you a second pop when the colony finishes it's initial development that initial colony group is only the race selected for the ship when building it. That way at least at first there's a good chance that the planet primarily populates for a time with the race selected rather than everybody else in the galaxy with a migration treaty with your empire.