Business rules get triggered after an action on the server, such as on Insert of the record...so as mentioned, you'd want to create a Insert BR for Incident table and then trigger your outbound REST with all the details. Then pick that up in your other instance, parse through it and then insert new record there.
Is there a reason why they need to be replicated in both instances, basically live like that? Are you all merging over to another instance or something? Do you have experience with web services/REST?
Regardless of my curiosity though, the basic gist of everything is above.
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