Assuming it is not the shunt causing it but the instantaneous trip unit that is casing this I would recommend changing the transfer switch programing to delayed transition.
What this does (if the ATS has the feature) is disconnect the load from one source then it waits for however long you program it for before reconnecting to the other source.
A quick transfer from one active source to another can cause breaker tripping. I believe the delay lets any supplied transformers or motors completely go dead before being energized again.
Any way adding a 1 second delay has worked for me in the past when customers had seeming random breaker tripping with transfer switch operation.