Usually you bring up Virtual IPs as an alias on one of your physical interfaces. For example:
ifconfig eth0:0 192.168.1.110 netmask 255.255.255.0 up
Which is exactly how you are supposed to bring up your "private IP" on Linode (I have an account with them too).
However, I'm not sure how this MMM script manages the Virtual IPs; from my brief look it seems that it is responsible for bringing up the Virtual IPs automatically on each machine, as it says:
I used the following virtual IPs. They
will be distributed across the hosts
But you may be able to assign private IPs to all your Linodes, and then add those IPs to the MMM configuration, as in their Installation guide, i.e. Use your Private IPs as the MMM Virtual IPs.
If you get stuck, the Linode support team seems to be very helpful, they've always got back to me within the hour.