"The rainy season starts in October."
Translation:Musim hujan mulai pada bulan Oktober.
I've seen this pattern with colors (warna hijau), days of the week (hari Senin) and times of the day (siang hari), but also with people (seorang profesor) and I've been told is common with other things wich are part of the same 'class'. I think it's called a classifier, but don't take my word for it in this particular case.
Also, I have no idea why they use it but it's common in Asian languages it seems. All languages have a level of redundance which makes it easier for the listener to follow the sentence (like verbs in English: that cat knows vs those cats know, if I said that cat know it would be, of course, wrong, but you'd get the idea... It's just a rule to help the listener follow the sentence). I suspect such a redundance was deemed necessary here by speakers of the language from the past :)
I did a bit of research before writing this and found a fun fact: it seems Bulan also means Moon and, by extension, satellite :)