Couple of things in play here, the Phenom 300 may be flown single pilot which I think may have been the case here since nobody else takes over the radios and the misunderstandings persist.
The decision to fly a trip single pilot or not are to the pilot. Busy Airspace, complex arrivals, anticipating language problems or weather issues…..bringing a second pilot would be prudent.
Secondly, this is a privately owned airplane and possibly owner flown? Which could mean we’re not dealing with somebody who is a career pilot.
Thirdly, the deviation took place in TRACON airspace which for the lack of a better word is a different jurisdiction then TWR.
Now I don’t know the ATC Controllers Handbook but it I am fairly certain that the deviation needs to be communicated by the ATC controller that has jurisdiction.
Like when you have a pilot deviation enroute you get the phone # of and by the enroute facility and not by by a tower controller maybe hours later.
As a final remark, the controller could have anticipated problems a little better, the foreign call sign is a bit of a giveaway as well as the subsequent hesitant answers.
So I’m going with 90% pilot and 10% ATC