meaning - What does "within a generation" mean in this context?

In a documentary film on the Russian Revolution the narrator used the phrase "within a generation", and I'm not exactly sure what it means.

Socialism promised peace, prosperity, and equality for all peoples of the world. But the social experiment failed. Millions were killed, and within a generation almost one third of the world's population was living in the shadow of communism.

I wanted to check a few figures about how many people lived under communism, but the phrase "within a generation" left me wondering at what period I should be checking populations figures. Generally I've had the habit of considering roughly 20 years for a generation. In some dictionaries and other sources it says a generation for humans is about 30 years. It also mentions this on Wikipedia.

generation
2.the term of years, about 30 among human beings, accepted as the average period between the birth of parents and the birth of their offspring.
Random House Kernerman Webster's College Dictionary

Anyway, in terms of that particular use of "generation", couldn't "within a generation" mean something closer to a person's average lifetime, say, 50, 60 or 70 years? The reason I'm wondering this is because, for example, say a group of people are born in 1960. Couldn't you say the 9/11 terrorist attack occurred within those people's generation? Even if they were 41 years old at the time it happened, and also notwithstanding that by that time another younger generation had been born?

Is that a reasonable use of "within someone's generation"?

Even if we take 30 years to mean a generation, the narrator's statement would mean that by about 1947 nearly a third of the world's population lived under communism. This just doesn't seem right. In 1947 the world's population was about 2.5 billion. One third of that is about 830 million. But we can't even include China (roughly with a population of 500 million), because it didn't become communist until 1949. Similarly the British Empire and/or India (it doesn't matter because independent India was never communist anyway) had a population of over 500 million, and when you consider the other most populous countries that were never communist this figure of "almost one third" really doesn't sound right. That is, of course, unless "within a generation" can be understood to mean what I mentioned earlier, roughly a group of people's lifetime, meaning it can extend to 40, 50, or 60 years. In that case I can imagine China's population explosion, along with other communist revolutions just maybe might bring it to the "nearly one third" measure used in the film.