I’m struggling to think of what part of the book you’re thinking of.
I’m on book 5 and 15 years have passed since the events of the first book. One of the characters says he’s 90, and they leave Earth when they’re 75. There’s no hundreds of years passing for anyone. The FTL travel is explained in a way without time dilation, but does have other side effects.
I’m being intentionally vague as Old Man’s War is one of my favourite book series and I enjoyed the reveal of the early plot points.