If I understand correctly, you only expect the atoms to move due to the fix deform when using the remap x option even if you use an integrator (which would be only the remapping with no other motions)?
Simply put, the fix deform remap x option tells LAMMPS that you want to remap the positions along with the box deformation. The addition of time integration will still give the atoms their own motions as determined by whatever integrator you choose to use. So, in result, you will be remapping the atoms and still maintaining their velocities, which sounds consistent with your description.
Note that I have not actually used the remap x option, so this description is based on my reading the documentation and using the remap v option. If I have some details wrongs, hopefully others with a better understanding will correct me.
Hope that helps,