Check Point has two things potentially called the "management interface", and neither has anything to do with SIC.
On branded boxes, one interface has a weird name: Mgmt. The MAC of this interface is used to uniquely identify the box in the User Center for support and licensing. The interface is not special in any other way. Unless you're using VSX, it's in the same routing table as all your other interfaces. I avoid using the interface named Mgmt because people expect it to be separate from the through-traffic interfaces.
On all systems, clish has a line in the configuration "set management-interface _____". This has no impact on how the firewall runs, it's not relevant to SIC, it's just a guardrail to prevent you from deleting the IP address.
SIC is just an application protocol which rides on top of the routing. The traffic will go over whichever interface the firewall's routing table says to use to reach the management, same as trying to ping the management server.