Did Roman command rotate from day to day?

Did command of a pre-Marian Roman army rotate from day to day?

No. In this case the serving consul outranked the proconsul, so Caepio was expected to obey Mallius.

The suggestion that command simply changed hands from one day to the next does not fit the hierarchy in this case. A serving consul stood above a proconsul. Former office or greater social prestige did not give Caepio lawful equality with Mallius while Mallius held the consulship. The battle's divided command arose from disobedience, not from an inherently rotating command system.