The short answer is that it is non-deterministic. Details below, and the usual workaround at the end.
The order that you receive ii_add_incoming_connection calls is essentially non-deterministic. Similarly, the order in which ii_push_record is called on each of your inputs is non-deterministic. It will depend on what the upstream tools do and how they are configured--so within a particular workflow it may appear deterministic, but it is not deterministic across all workflows.
So in some workflows you might receive ii_add_incoming_connection calls for each of your inputs before ii_push_record is ever called for any of them, and in some workflows one input might call ii_add_incoming_connection, a series of ii_push_records, and then ii_close before the other input is ever added. An example of where we might do the former would be two input tools--one input tool might open, pump all its records, then close, then the other input tool would do the same. An example of where the other might happen would be if your two inputs were the two outputs of a filter tool, where the ii_add_incoming_connections would happen about the same time, the ii_push_records would come in an arbitrary order on either input, and they would both close at about the same time.
Typically if records from one input require information from the other input before they can be processed you have to cache them somewhere and then pull them out once ii_close has been called on each of the relevant inputs.
