Certain firewall versions require the management run a jumbo equal to or higher than a certain version. This mostly affects managing newer minor versions. For example, R81.10 jumbo 82 adds the ability to manage R81.20 firewalls.
Some branded hardware requires a particular jumbo for management to be supported. For example, R81.10 jumbo 141 adds the ability to manage 9000-series branded boxes.
Fixes to some issues may need a certain jumbo to be on the management to affect how policy is built.
Other than those three situations, the management jumbo is mostly independent of the firewall jumbo. That said, updating a management is a lot less risky and a lot lower impact than updating firewalls. Why not do it first?