You're confusing the local observation time of a phenomena with the time the phenomena occurred as observed from our frame of reference and relative distance from its origin.

Special Relativity states that the time (component of spacetime distance) to an event depends on the relative velocity (angle) of the observing reference frame. It does not state that an event occurs at the moment it is observed; that would imply light has an infinite velocity.

The whole point of relativity is that events do not occur at the exact moment they are observed, because light has a finite velocity. The fact that light's finite velocity is the same in all reference frames is what causes reference frames to tilt their spacetime angle according to their velocity.

It's the same as saying the Y component (height) of a line segment changes if you rotate it. The length of the line is the spacetime distance, the height (Y component) of the line is time, the x component is spatial distance, and the angle of the line depends on the relative velocity of the observer.