This is a tough question. I don't honestly know if there was a single moment for collecting daylilies, but there certainly was a moment when I changed the type I was collecting (or hoarding). The first daylily I ever owned, was a gift from someone. It was SILOAM PEONY. I added a few others and was really happy with how resilient and hardy they were. Then I discovered forums and started searching more and more and was amazed by what I found. I thought it was nuts that people would spend $$$$$ on plants. I used to garden with my grandmother but she never had daylilies, and growing up in southern California we didn't have them in the yard either. It was really something I stumbled into.
Then I saw a picture of BLUE BEETLE and everything changed. I was mesmerized by the picture of it blooming as a double. Completely taken. When I saw a fan on the auction I had to have it because Jamie Gossard was sold out. That was it. It just spiraled from there. I still have BLUE BEETLE. It's a gorgeous plant. Hardy, increases well (I've sold and given away 8 or 10 fans over the years), and blooms reliably. For everything about the picture of the double, it has NEVER doubled for me. But I am smitten anyway.
I get a kick out of how my interests in daylilies have changed over the years. It makes for an evolving garden and I really enjoy it. I used to keep a list and really don't any longer. I just go with what suits me at the time.