Does Jack have an obligation to acknowledge Bob's contribution to the mathematical model? If so, did Jack satisfy this obligation? Would Jack's acknowledgment have changed if Bob had been in the audience? I think so. The idea that Jack developed in his model benefited from his work with Bob, it is natural and ethical that Jack should explicitly thank Bob for his contribution on this matter. He should mention his collaboration with Bob as soon as he mentions the aspect of his work that he has been working with Bob. To acknowledge Bob only at the end of the talk would prevent the audience from learning in what way Bob has helped with Jack's own work. Acknowledgment at the end can also be used for non-academic support, such as funding sources, and so on.
So Jack should say that the model he is presenting right now has resulted from his extensive collaboration with Bob. This will also help with Bob's own career prospect. Are decisions concerning attribution entirely Jack's responsibility? Should he consult others? How can one ensure that the work of professional colleagues is properly identified in an oral presentation? What, if any, were Hill's responsibilities in preparing Jack for his presentation? The decision is Jack's own to make, but he misjudged it when he started to mention Bob's help only at the end.
In this case he should consult others especially those who are more experienced in this kind of thing. Data sharing should be something that is consented by all parties involved. We can ensure that collaboration with colleagues is properly acknowledged through a program of study that sensitizes and familiarizes the student with overall ethical practices in scientific research. More directly, though, there should be ongoing seminars in the lab where everyone sits down together and discusses everything that they are interested in, especially ethical practices and also administrative ones -- in many cases the two go together. Who else does Jack have obligations to? What are these obligations? Does Jack satisfy these obligations? Jack also has obligations to the lab where he has been working. This is the case where he can acknowledge at the end of the talk. To what extent does a presentation at an interview resemble a publication? To what extent does it differ? It resembles a publication in that it is a presentation of research findings, so it has roughly the same oversall structure: introduction, objective, methodology, discussion, conclusion, and others. But since this is not a finished product yet it is not exactly a publication yet. Did Jack misrepresent his own expertise and/or his own work on the project?
What if his Ph.D. work had been all experimental and involved no mathematical modeling? Jack risks being perceived as misrepresenting his own expertise by doing what he did. In order to avoid the risk he should explicit mentions Bob and his contribution as soon as this topic comes out during the talk. If his Ph.D. work involved no mathematical modeling at all, then this is all the more reason to acknowledge Bob's contribution. The audience would suspect that Jack might not be able to raise the mathematical points on his own. What, if any, are the obligations of the interviewers? Should they probe Jack's level of expertise? Is the type of lab Jack comes from likely to influence their evaluation of Jack's work? The interviewers have an interest in finding the best possible candidate. And part of being the best candidate involves ethical conduct too. This is in the interest of the institution in the long run. They can probe Jack's expertise easily enough through a look at his transcript, his dissertation and his cv. It looks like Jack has worked in a prestigious lab, so this should reflect positively on his own chance of getting hired, so if he had acted properly regarding Bob's contribution, then the chance of his getting the job would be much greater.