Hi,
There are two ways you have to look at this
1. traffic till ce - pe
2. traffic after reaching Pe
traffic be it be control plane or data plane as you have righly put will land on PE device VRF instance. Now, there is a MP-BGP which runs between Two PE routers globally and MPLS LSP which runs between two PE routers. These global protocols help to transport traffice (control and data of Multiple VRF Instances) while protocols at CE/VRF Level will help to communicate between your CE and PE Devices , hence you have seperation of Global and Local at VRF level so that customers can be identified based on RD/RT