This is where his fellow scientists call him a "crackpot" because he can't replicate any of his experimental findings. ;)

More seriously, the sim could modify his observations to make him observe the right things. For instance, change the photons entering his eyes to be in line with what they should be, change the historical records a la 1984, etc. Or let him add an epicycle to his theory to account for the otherwise unexplainable results.

In practice, I doubt atomic-level effects are ever going to produce clearly observable changes outside of physics labs, so 99.99999% of the time the simulators wouldn't have to worry about this as long as they simulated macroscopic objects to enough detail.