The formation process of multiple populations in globular clusters is still up for debate. Kinematic differences between the populations are particularly interesting in this respect, because they allow us to distinguish between single-epoch formation scenarios and multi-epoch formation scenarios. We analyze the kinematics of 25 globular clusters and aim to find kinematic differences between multiple populations to constrain their formation process. We split red-giant branch (RGB) stars in each cluster into three populations (P1, P2, P3) for the type-II clusters and two populations (P1 and P2) otherwise using Hubble photometry. We derive the rotation and dispersion profiles for each cluster and its populations by using all stars with radial velocity measurements obtained from MUSE spectroscopy. Based on these profiles, we calculate the rotation strength in terms of ordered-over-random motion (v/{sigma})_HL_ evaluated at the half-light radius of the cluster. We detect rotation in all but four clusters. For NGC 104, NGC1851, NGC 2808, NGC 5286, NGC 5904, NGC 6093, NGC 6388, NGC 6541, NGC 7078 and NGC 7089 we also detect rotation for P1 and/or P2 stars. For NGC 2808, NGC 6093 and NGC 7078 we find differences in (v/{sigma})_HL_ between P1 and P2 that are larger than 1{sigma}. Whereas we find that P2 rotates faster than P1 for NGC 6093 and NGC 7078, the opposite is true for NGC 2808. However, even for these three clusters, the differences are still of low significance. We find that the strength of rotation of a cluster generally scales with its median relaxation time. For P1 and P2, the corresponding relation is very weak at best. We observe no correlation between the difference in rotation strength between P1 and P2 and cluster relaxation time.