I would say there is no difference in the scenario you described and in scenario with roaming.
So based on description given I will answer exactly the same way how it happens in roaming.
Now, depends on the roaming agreement we can see few roaming architectures
- scenario with home routed traffic local breakout, with home
- operator's application functions only local breakout, with home
- visitor's application functions only
Check the Fig. 2, Fig. 3 and Fig. 4 in http://www.lteandbeyond.com/2012/01/interfaces-and-their-protocol-stacks.html