Temporal Knowledge Graph (TKG) reasoning remains challenging to characterize with conventional flat representations due to its intrinsic heterogeneous structure. Existing multi-geometry approaches face two key bottlenecks: 1) the Riemannian depth barrier driven by numerical instability, which restricts models to shallow architectures; and 2) gate collapse, where adaptive fusion mechanisms suffer from gradient starvation and degenerate into single-geometry solutions. To this end, we propose MAGIC (Multi-geometry Annealing Graph Interaction with Consensus). Our framework introduces a Tangent-Residual Engine in multi-geometric spaces, which enables the first stable 8-layer geometric evolution and reveals a phenomenon termed Geometric Annealing, where manifold curvature spontaneously evolves from semantic flatness in shallow layers to structural complexity in deeper layers. We further design an explicit reasoning module with structural consensus, leveraging geometric invariants and structural priors to regulate gradient flow, prevent collapse, and ensure robust synergy across Hyperbolic, Spherical, and Euclidean spaces. Experiments show that MAGIC achieves state-of-the-art performance in TKG reasoning, improving MRR by up to 2.9 points.