You can do it either way. I remove the old filter, remove the small drain plug, clean inside the housing and prefer to add oil to the filter housing, (the top is off anyway when you change the filter). If you dont add oil to the filter, add the new oil, run the engine for a few minutes, shut it off, put away the tools then recheck the crankcase oil level. You will likely have to add a bit more oil to replace what is now in the filter.