I do not believe his situation is related to Routing-Instances, as there was no mention of them to start with. In regards to routing-instances, yes me.0/vme.0 can only reside in default routing instance (inet.0). I believe the issue is that that mgmt IP does not know that 192.168.129.1 is it's Default GW. This is not configureable with either me.0 or vme.0. Therefore if 192.168.129.0 is truely a mgmt ONLY VLAN, configure a static route for 192.168.129.0 to point to Next Hop 192.168.129.1 and then all should work. If there is another default (0.0.0.0/0) route, this route would be used for communication from vme.0 to anywhere else in the world. I assume right now the vme.0 is using that default route - you do have some default route configured, yes?
See this for more info on how to check for proper operation:
https://kb.juniper.net/InfoCenter/index?page=content&id=KB25724&actp=search