In the standard interpretation of special relativity, Minkowski space is viewed as an affine space. This paper argues that a tangent bundle (TM) is a more suitable mathematical structure. We show that the 4D "block universe" is a structural misinterpretation rather than a physical necessity. The standard eternalist view arises from an ontological reification error: the conflation of local tangent fibers (TpM) with the global manifold (M). While there exists a "trivial isomorphism" between a fiber and the base manifold, which allows Minkowski tangent space at a given location to be treated as a global affine space, this paper demonstrates that it is only permissible in Euclidean geometry. In the pseudo-Euclidean structure of relativity---where time functions as an evolutionary parameter along a worldline---this globalization leads to inherent ontological instabilities. By analyzing the Andromeda paradox through the non-compactness of the Lorentz group, we identify the projected temporal jump of distant objects as a "coordinate shadow"---a mathematical artifact of an indefinite metric rather than a physical displacement in a 4D manifold. This geometric deconstruction resolves the paradox without resorting to a frozen ontology, thereby restoring the physical viability of a dynamic, 3D-first reality.