Answer
The new raster that is created by the 'Mosaic to New Raster' model aligns to the raster corresponding with the option selected for the 'Mosaic Method' parameter. The default option is 'LAST', which results in the last input raster's cell alignment being the one used to snap the newly created mosaic. If 'FIRST' is selected, then the raster at the top of the list is used to define the pixel registration.