Conventional approaches classify symmetry-allowed magnetic configurations but do not by themselves establish a direct, mode-resolved correspondence with parent-lattice vibrations. Here, we formulate a universal determinant-induced pseudoscalar twist for all 32 crystallographic point groups, establishing an exact representation-to-geometry correspondence between parent vibrations and magnetic order. Within the paramagnetic gray group G×Θ_T, the spatial twist determines symmetry-defined magnetic geometry, while time-reversal parity independently specifies magnetic character. Each parent phonon irrep Γ maps to Γ_mag=Γ⊗Γₚₛ, preserving multiplicities and yielding the projection identity P_(mag,mn)^((Γ⊗Γₚₛ))=P_(ph,mn)^((Γ)) under the common Cartesian realization. This establishes the Template Principle: parent vibrational modes furnish real-space templates whose symmetry-enforced nodal manifolds are inherited exactly. Applied to monolayer Cd₂N₃, the framework identifies the ferrimagnetic ground state from the parent A₂ᵤ sector, confirmed by first-principles calculations, alongside cluster magnetic octupoles and antiferromagnetic manifolds. It further provides an a priori parent-group criterion for screening symmetry-allowed linear magnetic responses.