When both ATS's are in the "normal" position there shouldn't be an issue with adverse currents through EGC's because any load current drawn through a feeder neutral conductor will be supplied by its own transformer.
However, when the ATS's are in the "emergency" position, there will be some current through the EGC's of both feeders because the two ATS's each have a N/G bond and are fed by a common generator. The parallel path that is across the neutral conductor of one of the two feeder's from the generator must pass through the EGC's of both feeders and also the neutral of the other feeder. And so the impedance of that path will be quite a bit higher than the direct path through the feeder neutral conductor connected to the generator. But there will still be some current on the EGC's.