Intel CPU bug, how does this affect us?

It's probably feasible for a user to retrieve data from memory within the VPS container from other users.
Does this vulnerability impact both Linux and the virtualisation software?

It impacts basically everything. has a very good Q/A section.

We're monitoring patches that are being worked on and that have been released thus far. We use the live kernel patching system KernelCare on most of our infrastructure and and eagerly awaiting patches from them and more information in general.

As of now I've not seen any information about attacks happening in the wild and hopefully things will stay that way for a while since this was discovered by a white-hat group and details shrouded in secrecy.