When you configure Manager Access on a data interface, the FTD often defaults to using the existing system default gateway for that interface in its "management" context. Since you cannot change this gateway directly via the "show network" CLI or the basic interface settings, you must use Static Routes within the Cisco Secure Firewall Management Center (FMC) to override this behaviour.
check this guide :
https://www.cisco.com/c/en/us/support/docs/security/secure-firewall-threat-defense/222145-configure-manager-access-on-ftd-from-man.html
Avoid configuring via the CLI, since the FMC overrides some configurations.
You can deploy static content as an example; make changes as needed based on the setup.
To fix the gateway for your secondary management interface (Ethernet1/4):
Configure a Static Route in FMC: Navigate to Devices > Device Management, select your FTD, and go to the Routing tab.
Target the FMC IP: Add a Static Route specifically for the IP address of your FMC.
Interface: Select inf_MySite-inside (Ethernet1/4).
Network: Enter the specific IP of your FMC (or its subnet).
Gateway: Enter the internal gateway IP you want to use for the VPN path. and deploy the configure to FTD and test it