MPI mode should guaruntee separate random number seeds, so you should have separate threads doing the same thing using different random number trajectories. Their logs should be similar in structure but not identical in RNG-dependent numbers (score, etc). If the numbers are the same, the RNG is not set up correctly somehow…
A related issue is Rosetta reporting, say, 10 copies of a structure in the scorefile, but only one PDB of the same name. This is caused when you run either not-MPI executeables in the same directory (via mpirun or not), or if you compile a not-MPI-compatible executable in MPI mode and run it that way anyway.
If it’s literally log files and not results you are worried about, try the flag -mpi_tracer_to_file [filename], which will put N different logs in separately numbered files.
I think you might be asking, “Is Rosetta using MPI to accelerate individual results, or is Rosetta just running multiple independent processes so that I get 10 results simultaneously?” It is the latter; Rosetta just runs N independent trajectories and uses the MPI layer only to organize them for the filesystem (so that the output names don’t overlap).