Aims. The relationship between baryonic and dark components in galaxies varies with the environment and cosmic time. Galaxy scaling relations describe strong trends between important physical properties. A very important quantitative tool in case of spiral galaxies is the Tully-Fisher relation (TFR), which combines the luminosity of the stellar population with the characteristic rotational velocity (V max ) taken as proxy for the total mass. In order to constrain galaxy evolution in clusters, we need measurements of the kinematic status of cluster galaxies at the starting point of the hierarchical assembly of clusters and the epoch when cosmic star formation peaks. Methods. We took spatially resolved slit FORS2 spectra of 19 cluster galaxies at z ∼ 1.4, and 8 additional field galaxies at 1 < z < 1.2 using the ESO Very Large Telescope. The targets were selected from previous spectroscopic and photometric campaigns as [OII] and H α emitters. Our spectroscopy was complemented with HST/ACS imaging in the F775W and F850LP filters, which is mandatory to derive the galaxy structural parameters accurately. We analyzed the ionized gas kinematics by extracting rotation curves from the two-dimensional spectra. Taking into account all geometrical, observational, and instrumental effects, we used these rotation curves to derive the intrinsic maximum rotation velocity. Results. V max was robustly determined for six cluster galaxies and three field galaxies. Galaxies with sky contamination or insufficient spatial rotation curve extent were not included in our analysis. We compared our sample to the local B-band TFR and the local velocitysize relation (VSR), finding that cluster galaxies are on average 1.6 magnitudes brighter and a factor 2-3 smaller. We tentatively divided our cluster galaxies by total mass (i.e., V max ) to investigate a possible mass dependency in the environmental evolution of galaxies. The averaged deviation from the local TFR is ∆M B = −0.7 for the high-mass subsample (V max > 200 km/s). This mild evolution may be driven by younger stellar populations (SP) of distant galaxies with respect to their local counterparts, and thus, an increasing luminosity is expected toward higher redshifts. However, the low-mass subsample (V max < 200 km/s) is made of highly overluminous galaxies that show ∆M B = −2.4 mag. When we repeated a similar analysis with the stellar mass TFR, we did not find significant offsets in our subsamples with respect to recent results at similar redshift. While the B-band TFR is sensitive to recent episodes of star formation, the stellar mass TFR tracks the overall evolution of the underlying stellar population. In order to understand the discrepancies between these two incarnations of the TFR, the reported B-band offsets can no longer be explained only by the gradual evolution of stellar populations with lookback time. We suspect that we instead see compact galaxies whose star formation was enhanced during their infall toward the dense regions of the cluster through interactions with the int...