Default Route for NTP,SNMP, Syslog, Sflow

NTP, SNMP, Syslog, Sflow, remote authentication will always use the management default route unless a TMM interface has layer 2 connectivity to the IPs of those services, or you have a more specific route defined in TMM. Personally, I would recommend having the appropriate routes/firewall rules in place for the management interface to handle all of these management functions rather than TMM. If TMM interafces are down for some reason(License issue possibly) these functions won't work.