Pacific Institute interview questions

It was a three step process. The first was with the recently-hired HR manager, who was great, transparent and upfront. The second was with the hiring manager/would-be supervisor and one other colleague. It was a conversational interview, no assignments yet. I noticed some red flags during this second interview - I was constantly interrupted and corrected for small things (like a mispronunciation or use of a word the interviewer didn't like). My question about the further details about the strategy of the program was brushed off because "it was on the website", but I needed to further explain things stated in my resume and cover letter. I really think this was a reflection of the interviewer and not of the organization as a whole. I did make it to the final interview, where I needed to showcase a presentation; the have a good policy that allows interviewees to use a relevant presentation that they already have on hand from work or school, so I did not need to make a new one. This final interview involved those who interviewed me in the second interview plus a director. At the end of the interview, I was prematurely asked to send the HR manager my references, because in the end, I was not offered the position.