The subordinating conjunction 'cuando' isn't the trigger that calls for the usage of the subjunctive mood. Rather, it's based on two things.
1) If the main clause contains a command, the subordinate clause is cast in the subjunctive mood.
2) If the action or event in the subordinate clause has yet to be completed, the subjunctive mood is used. Conversely, when the action or event is completed or in process, the indicative mood is used.
In the example cited, the elderly person is the subject of the subordinate clause. They are 'boarding'. The action is in process, or has just been completed and the elderly person is now looking for a place to sit. Out of courtesy, we give up our seat. We don't generally do it before the need arises.
In the explanation above I also answered your second question. The elderly person is the subject in the subordinate clause, not the person being taught a courtesy lesson in the main clause.
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