Owing to the fully 3D topology of Multi-Linear Silicon Drift Detectors (MLSDD) and since the longitudinal coordinate is measured from the electron drift time, an accurate calibration of the relationship drift time vs. drift coordinate is needed and the dependence of the time-resolution and longitudinal position-resolution on the ionization profile has to be evaluated. In this work we performed a detailed qualification of the response mapping of one MLSDD prototype for different ionization profiles - namely 1 MeV, 3 MeV and 5 MeV protons and 705 nm and 904 nm IR laser. Probing the detector response with different ionization profiles allows performing a 3D mapping of the detector response. Moreover, thanks to the use of a custom deconvolution algorithm based on the conjugate gradient method, it is possible to extract the true shape of the current induced at the collecting anode from the preamplifier digitized output waveforms. The anode pulses provide detailed information on the transport properties of the detector allowing also to derive the effective longitudinal profile of the charge cloud that affects the position resolution measurements. Experimentally we measured a longitudinal broadening significantly larger (up to ∼1.5x) than in the case of free broadening.