correct. What you're bumping up against is the general theory of relativity.
Special theory of relativity deals with the behavior of different inertial frames moving at different velocities relative to each other. But then general theory adds in what happens when you accelerate and shift from one of those frames to another frame.
I can't pretend to understand all the math, but it is general relativity that both explains why it is the people in the rocket, if they turn all the way around and come back to Earth, who are younger than the people who stayed on Earth... And why we sitting down here in our gravity well experience time a tiny, tiny fraction more slowly than the GPS satellites orbiting the planet do. Because a rocket ship accelerating and the constant acceleration of standing around in a gravity field are exactly the same as far as the theory goes.