MC uses a concept called the Playing Now list. This is the playlist that is currently playing.
When you start playback from a particular list or view, MC adds the files in that list to this special Playing Now list, in the order in which they appear at that time. However, if you then later change the order of the source playlist, it doesn't change the playback order of Playing Now. They're separate.
To change the order of lists as they are playing, you can just change Playing Now. Switch to Playing Now in the tree and you can drag the items up and down, and re-order them however you'd like, and they'll play in that order.
If you want to save a particular list order, then you can change it in a Playlist. When you do though, to "see the results" you need to play the playlist. If it is already currently playing, you need to "play it again", in order to "overwrite" the current Playing Now list.