Is AssetsManagerEx already implement background downloading?

Does AssetsManagerEx continue download when user passes home button?

As of cocos2d-x 3.9 there is an iOS Downloader implementation that makes use of NSURLSession allowing downloads to continue in the background. If the user terminates (swipes up) the app, the download will end.

Yes if you’re using cocos2d-x 3.9 or above.
No if you’re using a version below cocos2d-x 3.9.