As it is stated in the header of the TIMESR.FIT files(keyword TIMEREF = LOCAL), the time values in the time series files produced by processing OM data in Fast Mode refer to the XMM-Newton satellite system.
This time scale can be converted into a solar system barycenter time system by applying the barycentric correction with the SAS task barycen:
barycen withtable=yes table=tserie.fit:RATE
where tserie.fit is the light curve file obtained from omfchain.
The barycen task overwrites the TIME column in the original file. Therefore, it is recommended to copy it beforehand if one wants to keep the non-corrected timing.
It should be noted that for OM, barycen is applied to the time stamps of the light curve, and not to the arrival time of each individual photon. barycen will not work on OM Fast Mode events list files.