All image based backup applications create snapshots of VMs, not just individual virtual disks. The only way to avoid snapshots of an individual virtual disk is to set it to "independent-persistent". Anyway, the reason this issue didn't occur with ESXi 4.1, but started with ESXi 5.1 is the fact that VMware changed the default location for snapshots. With ESXi 5.x snapshots of virtual disks are placed in their parent virtual disk's datastore, whereas in earlier versions they were created in the VM's "home" folder (where the .vmx file is located).
So your option is to either increase the datastore, or to follow VMware KB: Changing the location of snapshot delta files for virtual machines in ESXi 5.x
André