If you split a road around an island, you need to add oneway=yes to the new segments. You also need to ensure that the direction in which the way is drawn is correct (the iD editor has a reverse function).

Although this is not the case here, you also need to ensure that any other tags relating to lanes, sidewalks, cycleways, parking and verges are updated to reflect the newly split carriageway's features.

Tags added in https://www.openstreetmap.org/changeset/163011938