You are misunderstanding relativity. You incorrectly use the term "accurate perception" when in fact, the whole point of relativity is that every point of view is equally accurate.
If you want to work through this (I am a former Physics teacher), we should start with motion. Once you understand relative motion, understanding relative time is easier.
The first step is to imagine you are on a spaceship, let's call it spaceship A, in deep space with no other planets or stars around. The only thing you can see is another spaceship. You notice that the other spaceship, called spaceship B, is getting closer.
Here is the question. Based on the information I have given you there are three ways to understand the motion between the spaceships.
1) Your spaceship is moving toward spaceship B. Spaceship B is fixed in space.
2) Your spaceship is fixed in space and spaceship B is moving towards you.
3) Both spaceships are moving towards each other.
The question is; how do you determine which of these three statements are accurate? From your point of view, your spaceship wouldn't be moving (option #1). From a person on spaceship B's perspective her spaceship isn't moving and she can see you moving (option #2).
How do you determine which of these perspectives is accurate?