Transport Rule Storage and Replication

In a hybrid Office 365 and on-premises Exchange deployment, Transport Rules are not replicated between the cloud and on-premises instances.

Hybrid Scenarios

In the hybrid scenario, there is no replication of rules between your on-premises deployment and Office 365. Therefore, when you create a rule in your on-premises Exchange organization, you need to create a matching rule in Office 365. The rules you create in Office 365 are stored in the cloud, along with the rest of your Office 365 organization configuration, whereas the rules you create in your on-premises Exchange organization are stored locally in Active Directory. When managing rules in a hybrid scenario, you need to make sure that you keep the two sets of rules synchronized by making the change in both places, or making the change in one environment and then exporting the rules and importing them in the other environment.

Reference: Microsoft TechNet