The talk, and I'll say 'talk' rather than 'interview', was a lot closer to the former than the latter, with the POI telling me at the end that he was 'confident' that I would receive an offer later this week. I'm guessing this means that I've been recommended for admission and that the offer just needs to be approved by the grad school - that's a fair assumption, right?
The chat lasted about 30 mins and we talked about his interests and mine and how they overlap. He also gave me the opportunity to ask him questions, and I asked him about a couple projects that he is working on that I'm interested in. I also made sure to point out that I'd met one of his grad students at the conference I was at in December and worked in a mention of the paper that student presented on. He also asked if I like programming and about my mathematical background - nothing specific or technical, he just wanted to make sure I didn't have a fear of Maths, as he put it. He also repeatedly made it clear that all PhD students are guaranteed funding for 5 years - it almost seemed like he was trying to convince me that this school would be a great place to go to (as if I needed any convincing). Since I'm from a tropical country, he made a joke about the winters at this place and asked how interested I'd be in coming - seemingly gauging my interest in attending.
He also described the process to getting a PhD, in that there'd be coursework for 2 semesters and I'd be expected to start research by next summer. I asked if it would be possible to start research earlier and he said I could start from day 1 if I knew what I wanted to do right away. He explained that once I was admitted I would be free to choose any advisor I wanted, but also said that I could contact him before the fall for reading material or any advice I wanted. While pointing out the importance of selecting the right advisor, he made the analogy that is often made here, that selecting an advisor is like getting married to someone, since you're going to be working closely with them for several years.
Somewhere along the conversation he switched saying 'if you get an offer' in describing the process to 'when you get an offer'. Then at the end he told me I should look out for the offer later this week since he was confident that I'd get one.
I'm thrilled at the prospect of attending this school and I'm eagerly awaiting the official offer.
UPDATE (Feb 16): I received an email today saying I've been recommended for admission with funding at this school. An hour later, I received another email of admission with funding from another school I applied to. I'm living a dream.