Before I answer this in detail, I want to make sure I'm clear on my assumptions:
1. There are 4 hosts in the cluster, two on each side of the stretch. If this is the case, then all 4 hosts are primaries. (The first 5 hosts in any cluster are primaries, so you only get secondaries when there are 6 or more hosts.)
2. If the network goes down between the two sites, will the storage be split-brained as well? I'm assuming it does, based on one of your comments.
So, given site #1 has hosts A and B, and site #2 has hosts C an D....
If, after the split between site 1 and site 2, A and B can still heartbeat with each other, and C and D can heartbeat with each other then there is no isolation response attempted. Isolation responses only kick in when a host cannot heartbeat with any of the other primaries, and it also cannot ping its isolation address (usually the gateway(s)) for the network(s) that host is on.
So, what happens is that A & B at site 1 conclude that C & D at site 2 have failed. And vice-versa. A and B will attempt to power-on the VMs that were running on C and D, same for C & D -- they will try and power on the VMs that were on A and B. Now, because some VMs' storage are located at site 1 and other VMs' storage are located at site 2, some of the power-ons might fail, as the storage is not accessible. But as A&B will attempt to power on all of C&D's VMs and C&D will attempt to power on all of A&B's VMs (this is assuming that admission control allows all these power-ons) then each VM will end up powered on correctly on either site 1 or site 2.
Now for the ugly part -- if any of the VMs at site 1 lost their storage in the partition, or vice-versa, then the vmware-vmx processes that represent those VMs will still be running on the host(s) on the side of the partition that lost the storage, and there will also now be a vmware-vmx process representing the same VM running on a host on the other side of the partition that has now acquired a lock on that VM. None of this is an issue until the partition rejoins. That's when the behavior described by Elisha happens -- i.e. the VM will appear to bounce back and forth between the two hosts until the question about the lost lock is answered by pointing the VC client directly at the host. And as he pointed out, the question will be auto-answered by VC for vSphere 4.0 U2 and above.
-- Ron