Context. Recent observational and theoretical works have suggested that the Tully-Fisher relation might be generalised to include dispersion-dominated systems by combining the rotation and dispersion velocity in the definition of the kinematical indicator. Mergers and interactions have been pointed out as responsible of driving turbulent and disordered gas kinematics, which could generate TullyFisher relation outliers. Aims. We investigated the gas kinematics of galaxies by using a simulated sample that includes gas-disc-dominated as well as spheroid-dominated systems. We paid particular attention to the scatter evolution of the Tully-Fisher relation. We also determined the gas-phase velocity indicator, which traces the potential well of the galaxy better. Methods. Cosmological hydrodynamical simulations that include a multiphase model and physically motivated supernova feedback were performed to follow the evolution of galaxies as they are assembled. We analysed the gas kinematics of the surviving gas discs to estimate all velocity indicators. Results. Both the baryonic and stellar Tully-Fisher relations for gas-disc-dominated systems are tight while, as more dispersiondominated systems are included, the scatter increases. We found a clear correlation between σ/V rot and morphology, with dispersiondominated systems exhibiting higher values (>0.7). Mergers and interactions can affect the rotation curves directly or indirectly, inducing a scatter in the Tully-Fisher relation larger than the simulated evolution since z ∼ 3. Kinematical indicators, which combine rotation velocity and dispersion velocity, can reduce the scatter in the baryonic and the stellar mass-velocity relations. In particular, s 1.0 = (V 2 rot + σ 2 ) 0.5 seems to be the best tracer of the circular velocity at larger radii. Our findings also show that the lowest scatter in both relations is obtained if the velocity indicators are measured at the maximum of the rotation curve. Conclusions. In agreement with previous works, we found that the gas kinematics of galaxies is significantly regulated by mergers and interactions, which play a key role in inducing gas accretion, outflows and starbursts. The joint action of these processes within a hierarchical ΛCDM Universe generates a mean simulated Tully-Fisher relation in good agreement with observations since z ∼ 3 but with a scatter depending on morphology. The rotation velocity estimated at the maximum of the gas rotation curve is found to be the best proxy for the potential well regardless of morphology.