The exact scale might be transitory, but the issue won't be. Any society with a fertility rate below replacement will trend towards producing a larger elderly than youthful population. The lower the fertility rate, the higher this disproportion will be. Imagine you start with a population of 100 who were just born, and a fertility rate of 1. For simplicity, we'll assume everybody gives birth at 20 years old, and dies at 80:

Year 0: 100 newborns

Year 20: 100 twenties, 50 newborns

Year 40: 100 forties, 50 twenties, 25 newborns

Year 60: 100 sixties, 50 forties, 25 twenties, 12 newborns

Year 80: 50 sixties, 25 forties, 12 twenties, 6 newborns

Year 100: 25 sixties, 12 forties, 6 twenties, 3 newborns

Year 120: 12 sixties, 6 forties, 3 twenties, 1 newborn

There's always the same ratio people above a given age as there are below, for a given fertility rate, once an equilibrium is established. In cases where your fertility rate is above 2, this ratio will be below 1 (more young than elderly). In cases where your fertility rate is below 2, it will be above 1. Both relationships are exponential, not linear.

I think another interesting issue that demonstrates is the sort of exponential snap, the "demographic bomb", in fertility related issues. In spite of an extinction level fertility rate, the population nearly doubles to 187 by year 60, before suddenly collapsing down to 22 over the next 60 years.

And these are numbers that are not entirely out of question anymore in many places. South Korea's fertility rate has dropped to 0.84.

The non-transient condition is extinction of all western societies. That the same model is being exported to the developing world just means that the extinction will be general rather than localized.