But you look up the prepositions on and upon in McMillan, Oxford, Longman, Cambridge, or The Free Dictionary, you will know that these prepositions can be used interchangeably in many cases. See McMillan for details. One of these cases is when one thing happens immediately after another. Look at the following sentences:
Please report to the reception desk on/upon your arrival.
Upon/On arriving home I discovered that he had gone.
She was joyful upon/on seeing her child.
Similarly, you can say 'on/upon their visit' in the sentence presented by the OP, without any difference in meaning. However. the use of 'upon' is much more formal than 'on'.