In my previous post I have setup a very basic MPLS network. I will use the same setup to explain how exactly MPLS ensures QOS for packets which hit MPLS domain with a tag.
Following is the process which occurs when the plane IP packet enters the MPLS domain. Tags available in the IP field gets copied to the MPLS header in MPLS Experimental bit field.

And this is how the packet looks after DSCP tagger gets copied to MPLS EXP bit. Check the MPLS EXP bit in below packet.
This capture was taken between R1 and R2

Once the MPLS header is removed from the packet the packet looks like below :
This capture was taken between R2 and R3.

See that we have MPLS label removed and the original IP header is left with the tag with which it entered the MPLS network.