I do see the multipolygon in the link you shared but not  eally sure how you created it around the green or bunker. If I draw an area around green let's say I and tag it as fairway everything around the tagged green it should be a fairway? So how is the inner area marked as in that multipolygon? 
This is what I have been doing as when I map, this is for video software used for golf simulator. My process is let's say on a fairway there is a bunker and there is rough around the bunker, I would mark that as a bunker then map half way around the bunker from the edge of fairway leaving a gap to identify the rough, the map the other half of fairway around the bunker joining the points of the fairway, thus when I extract the data from OSM it shows up exactly like the golf course. 
If you are on discord I would love to do a video chat with you. I am on the OSM server under my name Dean.
How or what button are you selecting to create the multipolygon or do I just add another area and tag it as rough? The fairway will over rite the rough and the green will over rite the fairway. I am sure it is to do and minor change for me. I am done mapping the course for what I need it for. I get the lidar info from the ministry and use a tool to import game file, lidar and OSM into one file and then start the creation. 
Hope to chat with you, time for this old guy to hit the hay.