The measurement of 4D (i.e., 3D space and time) displacement fields of in situ tests within X-ray Computed Tomography scanners (i.e., lab-scale X-CT) is considered herein using projection-based Digital Volume Correlation. With one single projection per loading (i.e. time) step, the developed method allows for loading not to be interrupted and to vary continuously during the scan rotation. As a result, huge gains in acquisition time (i.e., more than two orders of magnitudes) to be reached. The kinematic analysis is carried out using predefined space and time bases combined with model reduction techniques (i.e., Proper Generalized Decomposition with space-time decomposition). The accuracy of the measured kinematic basis is assessed via gray level residual fields. An application to an in situ tensile test composed of 127 time steps is performed. Because of the slender geometry of the sample, a specific beam space regularization is used, which is composed of a stack of rigid sections. Large improvements on the residual, whose SNR evolves from 9.9 dB to 26.7 dB, validate the procedure.