"Furthermore, as virtual machine hypervisors transparently share memory pages between VMs [5,19], the attack is applicable across the isolation layer between VMs"
It's saying your VMs aren't safe - your Amazon/Linode/Rackspace/DigitalOcean/NineFold/Hertzner cloud instances _do_ have arbitrary users running arbitrary code on them – and the hypervisor can't protect you against what they do (in terms of manipulating the shared cache).
There have been cache side-channels demonstrated against some AES implementations, but this attack requires some bit of code whose "execution-or-not" (for lack of a better term) reveals some information the user would like to keep secret.
It is actually very worrying, since it might affect compression software (leak info about the file being compressed), text editors and other software that executes code based on key presses (cross-user keylogger), code whose execution depends on mouse actions e.g. button hover/click events (track another user's mouse), and so on.
Essentially, it turns all "if", "while", and "for" statements into information leaks.
I've written more about it here: