So each swim lane is an actor that interacts with your system. Its about the interaction between the actors and the system. By definition the system doesn't initiate anything on its own. In your example, you say the system displays local branches. It will only do that in response to an actor requesting it to do that. So its the actor initiating the activity that you want to show - something like Select Local Branch or something like that. The system validates the payment as a result of an actor doing something - perhaps Enter Payment or Submit Payment.

You have identified the activities that are happening, you just have the wrong names for them. To quote (badly) Atticus Finch in To Kill a Mockingbird, walk in the shoes of your actors when doing BPMN and your processes will be a lot better.

Kimbo