There are many kinds of fertilizers. That said, they do not just go off like that. This is so for ammonium nitrate, whose energetic chemical bonds are not particularly highly stressed, which means they are stable. That is why fuel oil is required to turn it into an explosive; it acts as a sensitizer and even then when one lights off ANFO, cursory post-event examination will show undetonated ammonium nitrate all over the place. In other words, it is not an efficient explosive agent. ANFO will only detonate via intense shock such as a blasting cap provides. You can light it on fire and it will not detonate, much as is the case with C4 and, IIRC, semtex.
Therefore, the plant probably went up by some other means. It is possible a dust explosion occurred, and those can be extremely powerful. If so, then there must have been a massive safety systems failure because this is a major issue for any facility producing finely divided combustible materials, wheat flour being just one example.
Perhaps we may keep an eye on this with some interest to see how the story evolves.
Speaking of which, I heard a rumor that the Boston devices were at least initially thought to have possibly been triacetone triperoxide. If so, then whoever is responsible is SERIOUSLY insane. It is a primary high explosive compound of highly strained and thereby unstable bonds. My understanding is that the synthesis path is VERY dangerous and as likely to kill the manufacturer as any intended targets. Has anyone else heard anything similar?