Existential inertia and spacetime

According to the principle of existential inertia:

1. If x exists at t₁ and t₂ > t₁ and there is no cause of x’s not existing at t₂, then x exists at t₂.

This sounds weird, and one way to get at the weirdness for me is to put it in terms of relativity theory. Times are spacelike hypersurfaces. So, then:

2. If x exists somewhere on a spacelike hypersurface H₁ and H₂ is a later spacelike hypersurface and there is no cause of x’s not existing on $H_2, then x exists on H₂.

This seems weird to me. Why should being in one specific area of spacetime metaphysically push one to exist in another specific area of spacetime? I can see how existing in one area of spacetime could physically push one to exist in another. But metaphysically? That seems odd.