It is a consistent unit of measure, but what everyone measures as a second is relative. The same thing is true for lengths.

Your misunderstanding comes from your thinking there is such a thing that "actual time has elapsed". Not everyone's second ticks at the same rate, and there's no way to say that mine is more valid than yours. But to the person actually on the ship they still feel like time moves "normal" since every physical process is dependent on the local flow of time.