A generation is about 25 years.
He was using a bit of hyperbole - but it was actually 1878 years from the destruction of the Second Temple until Israeli independence in 1948. It is more like 75 generations (or 62, if you count a generation as 30 years), but 100 is more poetic. Also, I am sure that some families have had 100 generations - marriages used to be a lot earlier in life than right now.
Think Purim.
You might be right about the hyperbole but if you consider that Israel was under ROMAN rule for some time before the temple was destroyed, and under Greek rule before that, then the generations are closer to 100.
While she was under foreign rule, she had no authority of her own.
I’m not familiar enough with how long the Roman’s ruled, or how long the Greeks ruled, or how long any other nation ruled to be able to give specific numbers. Perhaps someone else can.