There are some differences in the track and cluster time distributions between data and MC that needed to be addressed.
The simHitTimeOffset introduced in SvtDigitizationWithPulserDataMergingReadoutDriver shifts the time of the simulated signal (tritrig, wab) hits with respect to the pulser hits. This is needed to mimic the turn-off of the track time distribution in data. This value can be set in the readout steering file and should be around -10ns.
The additionalShift introduced in EcalTimeCorrectionDriver globally moves the ECAL cluster time. This is needed to put the time peak in MC at the same time as in data to avoid cutoffs introduced at other points in the pipeline. Without the shift, the cluster time in MC peaks at 24ns, in data at 37.3. So the shift should be 13.3ns.
Note: I have tried shifting both cluster time peaks to 0ns, however this breaks things since there is a hard cut at 0ns that is implemented somewhere else. Matching data and MC appears to be the safer approach.

I have also changed the tsCorrectionScale value in the RawTrackerHitFitterDriver setting to the value needed to match MC to data. This correction scale globally shifts the hit time of pulser and simulated hits in the pulser overlayed-MC sample.