Use ssh with a specific network interface

It's not the ssh client that decides through which interface TCP packets should go, it's the kernel. In short, SSH asks the kernel to open a connection to a certain IP address, and the kernel decides which interface is to be used by consulting the routing tables.

(The following assumes you're on GNU/Linux; the general concept is the same for all Unices, but the specifics of the commands to run and the way the output is formatted may vary.)

You can display the kernel routing tables with the commands route -n and/or ip route show.

OpenConnect should have added a line for the tun0 interface; connections to any address matching that line will be routed through that interface. For example, running route -n on my laptop I get the following output:

Kernel IP routing table
Destination     Gateway         Genmask         Flags Metric Ref    Use Iface
0.0.0.0         10.30.0.1       0.0.0.0         UG    0      0        0 eth0
10.30.0.0       0.0.0.0         255.255.255.0   U     1      0        0 eth0
169.254.0.0     0.0.0.0         255.255.0.0     U     1000   0        0 eth0
192.168.122.0   0.0.0.0         255.255.255.0   U     0      0        0 virbr0

This means that connections to hosts in the 192.168.122.0/24 (i.e., addresses 192.168.122.0 to 192.168.122.255 according to CIDR notation) network will be routed through interface virbr0; those to 169.254.0.0/16 and 10.30.0.0/24 will go through eth0, and anything else (the 0.0.0.0 line) will be routed through eth0 to the gateway host 10.30.0.1.

I don't know when it was introduced but the OpenSSH client on RHEL7 has this in its manpage:

 -b bind_address
         Use bind_address on the local machine as the source address of the connection.  Only useful on systems with more than one address.

Not as good as being able to choose the interface, but close.

Just addition of an Answer. You can use -b flag and define your source IP at access time.

Format + Example

ssh -b interface-ip remote-ip
ssh -b 10.11.22.40 10.11.22.38