As the Reliant was the first ship to do a close range inspection/examination of the system and its planets, it is possible that the audience is meant to assume they believed the fifth planet of the previous long range scan was the one that blew up, and initial appearance of the planet still present matched the long range scan. It's quick and dirty, but it makes sense on a storytelling level.
I've long understood the Ceti Alpha system to have many more than six planets, as well. And to Christopher, who said that the system was actually the one we have named Alpha Ceti; Says who? As far back as TOS, they probably wanted to avoid such disparities as the one you cited, and thus changed the name. No one ever said system names had to be alphabetical within the name itself, so Ceti Alpha is different than Alpha Ceti. Different name, different system.