The practical applicability of the rare-earth doped scintillators in high-speed detectors is limited by the slow decay components in the temporal response of a scintillator. The study of origin and properties of material defects that induce the slow decay components is of major importance for the development of new scintillation materials. We present a table-top, time-domain UV-VIS luminescence spectrometer, featuring extended time and input sensitivity ranges and two excitation sources. The combination of both soft X-ray/XUV and UV excitation source allows the comparative measurements of luminescence spectra and decay kinetics of scintillators to be performed under the same experimental conditions. The luminescence of emission centers of a doped scintillator can be induced by conventional N₂ laser pulse, while the complete scintillation process can be initiated by a soft X-ray/XUV pulse excitation from the laser-produced plasma in gas puff target of 4 ns duration. In order to demonstrate the spectrometer, the UV-VIS luminescence spectra and decay kinetics of cerium doped Lu₃Al₅O₁₂ single crystal (LuAG:Ce) scintillator excited by XUV and UV radiation were acquired. Luminescence of the doped Ce³⁺ ions was studied under 2.88 nm (430 eV) XUV excitation from the laser-produced nitrogen plasma, and compared with the luminescence under 337 nm (3.68 eV) UV excitation from nitrogen laser. In the former case the excitation energy is deposited in the LuAG host, while in the latter the 4f–5d₂ transition of Ce³⁺ is directly excited. Furthermore, YAG:Ce and LuAG:Ce single crystals luminescence decay profiles are compared and discussed.