[ExodusUK]

The term "producer" is so ambiguous in Jpop lol. Before she was credited as "Visualised by" then produced with Max and then just Ayu as the producer though her role probably didn't change that much as she's always been involved with everything from the start.
The "Executive producer" is the one typically in charge of money/business/etc while a "producer" is creatively involved in a project. Ayu has never been credited as an "executive producer", the Executive Producer on Power of Music for example is Max Matsuura.

It's different for Avex and Japanese stuff, US acts tours are handled by an outside company like Live Nation or a sponsor who have a contract/deal with the artist and not the record company. All of Ayu's tours are managed/handled inside Avex by Avex Live Creative. What I imagine is that Avex fiances the concert. Ayumi gets a nice percentage, Avex takes a percentage and a percentage is used to pay crew/dancers/etc. But this is all guess work, no one can know for sure unless they've seen Ayu's contract. Even elements from Ayu's staging and such have been reused in A-nation and other Avex acts like Koda Kumi's disco ball thing from the dome tour from the top of my head.