Here is an outline of the configuration:
Host A
2 nics, one goes to standard network, second to private esx network

Host B
1 nic, goes to private esx network

The two hosts can reach each other just fine.
And host A can reach the outside fine as well.

I'm going to be running stress tests between host A and host B, so I need to ensure the standard network does not see any of the traffic.

How does linux figure out what nic to go through when I type something like ping hostb?

What can I do to ensure packets for hostb always go out the right nic and never try the wrong one?

you can use:

ping -I eth(x) (ip address)

to indicate to ping which interface it should use to send ping traffic.

If you have your routing table set up correctly, the traffic should exit on the proper interface. Actually, if you have your routing table set up right, you shouldn't need to use '-I eth(x)'.

Thanks, I thought routing tables were the way togo but my quick browsing on it didnt seem right. I'll keep reading.