Production of the movie started right at the end of the lengthy recording sessions (reminder that Discovery started being a thing late into the Homework recording sessions, with Short Circuit & One More Time being early productions) but it's rather uncertain how this process started. The one thing that I'm 100% sure of, is that the entire production was funded by DP themselves, and they are probably the only owners of the golden master of the movie. (Hence their media team's fault about the absolutely crappy 4K remaster and noise around it, that led to that awful Epic collaboration).
Singles were released at rather odd intervals for Discovery in particular (according to Bangalter, all songs were conceived as potential singles) and music videos were released after the singles.
EDIT : To be honest, it's a bit tricky to be 100% sure about the actual process, with most of the claims being unsourced random internet shenanigans, and the tendency of some people (hi Pedro) to rewrite history whenever they wish.