Hi Pedro -
No, the different input rasters do not need to be in the same resolution. If they are not, the model will resample them all to be the same, but the rules are a bit different for different models. I mainly know about the freshwater models (annual/seasonal water yield, NDR, SDR), so if you have a question about others let us know and someone else can respond.
For the freshwater models that use a digital elevation model (DEM), the other input rasters are resampled to match the DEM, since resampling the DEM can change the hydrology, and that is considered the most important to preserve. For annual water yield (which does not use a DEM), all rasters are resampled to match the land use/land cover, since it is considered the most important.