Differential Interferometry allows to obtain the differential visibility and phase, in addition to the spectrum. The differential phase contains important information about the structure and motion of stellar photosphere such as stellar spots and non-radial pulsations, and particularly the rotation. Thus, this interferometric observable strongly helps to constrain the stellar fundamental parameters of fast rotators. The spectroastrometry mainly uses the photocentre displacements, which is a first approximation of the differential phase, and is applicable only for unresolved or marginally objects. We study here the sensitivity of relevant stellar parameters to the simulated photocentres using the scirocco code: a semi-analytical algorithm dedicated to fast rotators, applied to two theoretical modelling stars based on Achernar and Regulus, in order to classify the importance of these parameters and their impact on the modelling. We compare our simulations with published VLTI/AMBER data. This work sets the limits of application of photocentre displacements to fast rotators, and under which conditions we can use the photocentres and/or the differential phase, through a pre-established physical criterion. To validate our theoretical study, we apply our method of analysis on observed data of the edge-on fast rotator Regulus. For unresolved targets, with a visibility V~1, the photocentre can constrain the main stellar fundamental parameters of fast rotators, whereas from marginally resolved objects (0.8<=V<1), mainly the rotation axis position angle (PA_rot_) can be directly deduced from the vectorial photocentre displacement, which is very important for young cluster studies.