Bit Confused on how tag popping works

Hey,I've been reading about this subject after I've encountered this in my work. Right now my job is to configure interfaces for our customers, specifically for circuits were we need to buy transport from another provider to get to our network.

The configuration on interface is something like this on the interface we receive the traffic from:

service instance 200 ethernet

encapsulation dot1q 100 second-dot1q 200

rewrite ingress tag pop 1 symmetric

then, we create a pseudowire pointing to a loopback interface on the router that will deliver the traffic to the final operator and, create a cross connect to put together service instance and the pseudowire.

Then on the interface we deliver it to the operator, the configuration is the same minus the tag popping bit.

My understanding is that, traffic arrives to us using the vlan 100, we pop the tag the moment the traffic enters our network and add our own tag to it (200)and then it travels through our network solely using the 200 tag, since this is the same vlan the operator we deliver it to expects, that's it, no further configuration is needed.

However in certain case we do use a vlan translations and the way we go about it is that in the point where we receive the traffic we pop both tags with the "rewrite ingress tag pop 2 symmetric" command, rather than just one and on the interface we deliver the traffic we configure the encapsulation with the vlan the operator expects and a "rewrite ingress tag pop 1 symmetric" command.

My question is, when the packet get to our network, it is composed by a customer vlan (with a value of 1-4096 we don't know about nor we really care) then the operator that delivers the traffic to us adds its tag then, we add ours once it enters our network as we pop the one added by the previous operator.

However, when the vlan is translated, we pop both so that means the information will travel our network without any tag, so my question is, once it gets there how does the destination router knows which service instance that packet belongs to (after all the tag for it was stripped the moment it entered our network) and how to retag it?

Does the router just sees which VC id it came from and thus is able to determine the interface service instance by looking at the crossconnect the pseudowire belongs to and once he sees the physical interface/Service instance associated to it knows what to do or, it does it in another way?

Thanks