Will need more info about the setup. If possible, you may paste a flow diagram along with dummy ip addresses.
anyways. following is something i understood.
1. You seem to be having Internet links on SSG.
2. SRX and SSG are connected via single L3 interface which caters to management as well as transit internet traffic.
3. To have the same working, you had to put a static default route on the SRX as it is the default gw for wifi users.
4. You wanted to have seperate management traffic as well as seperate transit traffic so that management traffic do not use the default route pointed towards the SSG.
5. You can create a sub-interface on ssg and assign a vlan-id to it for management. You can extend the same vlan till srx and put the controller's management as well in the same segment. That should suffic for forcing management traffic not be routed on trasit interface.