How can it go faster? Pop increase hasn't changed. The idea was, afaik, that regions with really low population would attract immigrants to increase pop rate... So if you're the 'source region' your population will increase slower than it did before.
It goes faster because of how population growth is determined as a function of existing population. Let's assume we have a city with a max pop of 60K, current pop of 40K next to a rural with a max pop of 8K, current pop of 300. Those 300 only produce a couple of new people a day, and the rate of increase is slow, and the region would fill up in months that way. City adds hundreds, maybe even a thousand to its pop every day, fills up in a few weeks, and then all those people potentially making new people don't actually provide any increase. With the immigration code, the city effectively continues producing new people for the depopulated rural. City takes a little longer to hit max pop, but the rural goes up a
lot faster.