The fact that they can't tell which one is time dilated by observing only relative motions doesn't mean there isn't real time dilation for any of them. All relative motions come from absolute accelerations, so there's an underlying objective state of different time dilations they can't observe. But by tracking the changes in motion of all the other entities in the universe relative to a given initial situation, they can keep track of who is really more time dilated, which explains the outcome of the twin paradox.

So you're right that time dilation doesn't change with speed. It changes with changes in speed, but the new time dilation you get doesn't go away when you stop accelerating, it's really there at the new constant speed you reach, only you can't tell how much time dilation you're experiencing just by measuring relative motions, unless you can compare those motions to some previous motions (internal or external) that can tell you by how much you accelerated.