It has nothing to do with acceleration. You can play games with acceleration and start to get "wrong" answers with the twin paradox.

What actually matters is who travels the longest World Line a.k.a. the longest path in 4-d spacetime https://en.wikipedia.org/wiki/World_line . That is all.

A person on a non-curved geodesic spacetime path ages more quickly than a person on a curved non-geodesic spacetime path