It doesn't really care. Time dilation is the natural consequence of the universe having laws that are true in every reference frame. 'Relativity' is a misnomer - it's really a statement about the absolute nature of physical laws.
Right; the word "relativity" comes from the concept that the laws of physics should be consistent in all frames of reference. That concept -- i.e., that when you're on a moving train, you toss a ball up and catch it, and it's the same physics as if you're standing still -- people seem to "get" quite intuitively.
What's weird about Relativity is that our experience leads us to expect that things like distance, mass, and time will be the same in every frame of reference. Instead, what's apparently the same in every reference frame is "how fast light appears to travel"; and that distance, mass, time actually warp to cause this law to be true.
If you take an equation from physics (like the mass-energy equivalence) and rearrange it to solve for t, you don't seem to get anything that makes any kind of intuitive sense. Time is very confusing.
