In the BP_Relevancy_Replication_Combined Blueprint's Event Graph, as seen in the commented section below, the OnChestTouch is overriden to use a combination of a RepNotify variable and a Multicast replicated function.
Properly displaying the chest has two components: one that is instantaneous (the gold particle) and one that is persistent state (the lid being open). The Multicast is employed to handle the instant event, while the RepNotify variable handles the persistent state.
Below is the OnRep function called when the variable bChestOpened is updated.
Click for full view
This example solves the issue we are presented and demonstrates proper usage of Multicast funtions and RepNotify variables. The result is what one would expect to occur when opening the chest in a networked game.