The whole immigration mechanic is not working, please check its turn count condition and you will know why.
What's more, I managed to fixed it on my own, but just discovered that immigration is not fun, but a bit annoying. First, immigration is determined by your population, happiness and health, the latter two are always terrible in industrial age because of factories and corps. And a large population will not discourage, but encourage immigration. So, there's less you can do to stop your population from moving out (like selecting certain civic to encourage or discourage migration). Second, immigration is too often to happen, making your population lost too frequently. Third, there's nothing about RNG, so the most favorable city is always chosen to immigrate, until their population is 'punished' enough. A bit of randomness could improve the flavour of gameplay. Finally, defining immigration as old world to new world is both not fun and ahistorical. It always punish old world civ and reward new world civ, regardless of their own situation. In our timeline, immigration flows from Mexico to America, from Middle East to Europe, from eastern bloc to wesern, etc.
So to speak in general, I advice that immigration mechanic should be revised before we fix the trivial bug and put it in game again. The crucial reason is that it's a bug that made it not working at all, so nobody (including me) is actually playing the game with the mechanic, and we couldn't tell it's impact on late game, it's balancing issues and so on. Another reason mentioned before is that it's not anything but an inevitable punishment to all old world civ, by regularly wiping out their population of several cities. To make the mechanic more fun, there should be both gain and lost, or there should be diverse strategies for player to trade-off, like we're deciding to whip population, close border or build baths during a plague.
*Edit: What I could share (from my limited experience) is that population is very valuable in late game. Both tiles and specialists are yielding much more than early game, and you need more and more food as your population grow. Thus, regularly wiping a population in your megacity is much more a punishment in late game.