And even then, I believe iOS determines if and when a background update occurs - even if an app requests it.
Sometimes, it depends on the activity.
Background tasks that are started before the app is minimized continue instantly (assuming they use the proper apis).
Background tasks that are scheduled to start at some time after the app is closed depend on some other parameters.
For example, downloads and uploads continue until complete.
Background App refresh is determined by how often a user accesses an app, and is designed to update the app before the user accesses it, so the content is already current.
Apps using Apple's background push service are also near instant, regardless of whether or not the app was used recently.