I have no idea what multiple managers can achieve, and I wasn't suggesting you to have multiple managers. I was just remarking that *if* for some reason you need multiple managers, passing the manager as a parameter would be the way to go as passing parameter provides the most flexibility out of all the other options. This goes for other similar situations as well.
Like BitMaster said, a static variable in a class is just like a global variable outside a class. It may be what you need if you are very sure you will only need one manager.
I don't have much to say about your quadtree, since I don't know much about using quadtrees and ECS together. I remember L.Spiro has an article on efficient quad trees though. Here it is: http://lspiroengine.com/?p=530