I am not surprised that it looks like low fertility follows after low child mortality. In this animation, most countries move left (low risk of child dying) before moving down (fewer children per woman):
This has let to this change in demographics:
Or, in other words, we don’t get more children, they stop dying. Almost all children will grow up to be productive adults. Nearing 2100 the number of children is expected to fall and previous estimates that the global population will max out at 11 billion people are now considered too high. We might end up with a global population of 9 billion people, even though it tripled in the 70 years since 1950 from 2.5 billion to 7.5 billion.