Are you saying that if I have multiple NICs in a given machine, that I need to assign each one of them a (unique) static local address, and then specify that static local address with the 'local host' option instead of using an identifier, such as eth0 or tun0, of the interface that I want to use with a particular instance of the OpenVPN client ?
yep. currently it's not possbible to bind OpenVPN to an interface.
However, as you're using Linux I'd go for some iproute2/iptables magic instead: use source routing to ensure that traffic intended for server1 leaves NIC1 and traffic intended for server2 leaves NIC2 : that way you don't need to specify anything in the config files, and have the kernel routing tables take care of it.