If you want the VSP to IP route traffic between VLANs, then you will need to configure an IP address on the VLAN itself (interface vlan X).
If you have a mgmt vlan IP (mgmt vlan) this does not do any IP routing. Note that if you have mgmt vlan IP x.y.z.1 as mgmt vlan 11, then you can also configure that same IP x.y.z.1 under "interface VLAN 11" as well. This will solve the routing between VLANs.
But the mgmt vlan IP will only ever be able to receive traffic from VLAN 11, not from the other VLANs.
If you need a mgmt IP to be reachable from all 3 VLANs, then create a "mgmt clip" instead.