So your question is what is real and what is perspective and what does perspective say about reality if it isn't itself real. Let's just use distance perspective as an analogy. Why do things seem to shrink as they move away from you? They don't really shrink. But what would reality look like without perspective and everything remained the same size no matter how far away it was from you. Your field of vision would be constantly overloaded with information and big blocking things. So why do things look smaller from a distance. It's because less and less information is reaching your eye. The information is still there and you can access it by zooming in on it with a telescope. This makes things at a distance seem big again.
The same is true for time. As things move away from you, the rate of their movement affects the rate of information transfer back to you and hence their time rate you see. Their time rate isn't really affected at all but your perspective of it is. But if you change the relative velocity at a distance, it will take time for them to see the new rate of information transfer you're sending. Time must be conserved, there can't be any discontinuities of missing time and there can't be any imbalances of stored info that does not sync up.
If you have been moving away from me at .6c, you will store .25 yrs of info for every yr you move away. If you turn around after 4 yrs, you have 1 yr of stored info that has not been transferred back yet. For every yr you move back, you will also be storing .25 yrs but that's easy to shed because your movement back doubles the normal info transfer rate. But this is still not enough to transfer all the stored time your movement has created so that you can sync up your normal time rate with your partner when you meet up again. Relativity (not Einstein's version but my own) takes care of this problem of information imbalance during the relative velocity imbalance after a change in velocity. During this time, which is 3 return yrs in my example, you will be actually travelling through time at twice the normal rate although you will not see anything but the normal rate of time in your own frame. Your return doppler shift ratio = 2 will no longer just be a perspective of information transfer but it will become a real movement through time at a rate other than the normal rate. Without this correction, there would be no way to clear the backlog of information created during the velocity change and the time the news of the change reaches the other party.