The collective precession of magnetization manifests itself as magnon modes. These modes are governed by complex-valued vectorial eigenfunctions, which have remained experimentally challenging to observe. Here we introduce X-ray magnetic vector chronoscopy (XMVC), a time-resolved resonant scattering method that reconstructs the full magnetization dynamics with angular resolution of 0.1° (±0.01°). Applied to a synthetic antiferromagnetic multilayer (Si/NiFe (8 nm)/Ru (0.8 nm)/CoFeB (5.5 nm)), XMVC enables magnon state tomography, by directly measuring the nanoscale vectorial eigenfunctions of hybridized modes arising from magnon–magnon coupling. This approach provides full access to the system’s non-Hermitian Hamiltonian, revealing the complex-valued coupling strengths and non-orthogonal eigenbases. These results establish XMVC as an experimental platform for studying nanoscale spin systems by extracting the eigenfunctions of the system.