Is a bile jar guaranteed to spawn before map 4's crescendo event in Dark Carnival?

A friend and myself ran DC on expert (trying for the achievement) for months. Most of the time, we got a single bile jar towards the beginning of the first map, but aside from that, no, it's not guaranteed. There were several (and it was like 15-20% of the time) that NO bile jar spawned at all, making that gate run near impossible. Knowing it's importance, we'd always keep an eye out for the jar, and seems highly unlikely that we'd just miss it that many times.