802.1Q Tunneling (Q-in-Q) Configuration Example

What happen if we have two customers, customer X and Y and use the same SVLAN (outer vlan) 123 and we segregate traffic using different cvlans (cvlan 12 for customer x and cvlan 13 for customer y). So, we have customer x site 1 and site 2, both sites using lan switches connected to the metro ethernet service provider lan switch and the same for customer y.
If customer X Lan Switch sends a BPDU towards the ISP, this BPDU will be carried on the inner vlan ? or should I have to configure the “l2protocol stp” on the interface configuration mode on the ISP edge interface between customer and the ISP ?