Just as a followup, in case anyone has any experience with this. I was recommended to add a multicast event for the “set tile” node. This **does **update the tile map for clients, but they generate a different room layout to the server. Which makes me think there is either a bug in my blueprints, or having so many multicast events firing in a loop is a bad idea 
It also throws a runtime error:
Blueprint Runtime Error: “Accessed None trying to read property BGTilemapReference”.
(BGTilemap is the name of the actor that contains the tile map)
I would have thought that if the actor is replicated then a multicast event shouldn’t be required, but maybe I’m wrong? Does anyone have any suggestions on this?