Remote Logging Throught Management IP

If i set the gateway, the logs will be sended by default through the mgmt ip? It doesn't need any other change?

Yes, you will need to define a route thru the mgt gateway. This will take precedence. Here is an example:

create sys management-route snmp network 20.2.2.2/32 gateway 10.1.1.1 (this is an example)

sys management-route snmp_route { gateway 10.1.1.1 network 20.2.2.2/32 }

Ensure that you are seeing the source ip of the mgt on your syslog server after events are generated.