Just going to throw my two cents worth in here too.
First, the best way I find to think of the Meraki Management interface is a virtual interface. The virtual Management port is an access port that then connects via a virtual cable to a virtual port on the switch (which is an access port), and whatever you specify as the management VLAN is the VLAN assigned to that virtual access port on the switch, not how the virtual management interface is configured. (Now I re-read that I'm not sure if it will help or not...)
Second, as @GIdenJoe states the management VLAN doesn't have to be the native VLAN. But, it makes it significantly easier if the management VLAN matches the native VLAN on the uplink. Since the virtual port behaves as an access port the traffic is never tagged. Its only when management VLAN traffic exits the switch on a trunk that it is tagged, if that VLAN isn't the native VLAN. As everyone has said, using the native VLAN is easier as when a switch with no configuration first comes up it, well, has no configuration, so the traffic from the management port will always access the switch untagged. Likewise, if you move the switch to another network if the management VLAN corresponds with the native on the uplink then it will more likely get a DHCP address (and thus retrieve its new configuration), even if the upstream port is configured as an access port, or is blocking certain VLANs.
Third, and completely unrelated to the management port. Remember that the MS390 runs a single instance MST, whereas a Catalyst switch will likely be running PVST+. This is just something to be aware of, and keep in mind if you appear to have STP issues.