First of all, let me clear the term for you. The correct term is 'VPS hosting' and not cheap VPS hosting. 'Cheap' has been added to it just for the sake of marketing the VPS hosting packages
A VPS is a Virtual Private Server and hence it is offered with root administrator access and guaranteed resources. The only resource shared between the VPSs created on the same dedicated server are the CPU resources. Hence, if you choose a reliable hosting provider who does not overload the dedicated server with too many VPSs and keeps enough resources for reserve on each dedicated server, you shouldn't face any problem with the VPS
