Well, there's no real intermediate varieties to look at.

So I'll talk about how such changes generally occur.
Changes to things like word order or gender are not usually sudden and universal— people don't decide one day to make all prepositions into postpositions. They proceed piecemeal, perhaps starting with a single Trojan horse. (As an example, in Konkani the word 'girl' is neuter, and that's led other words for young women to become neuter, while words referring to older women remain feminine. In Old Chinese, locatives were normally <noun> <locative>; this became <coverb> <noun> <locative><classifier>, but there is still a good deal of variety. Still <coverb><noun> seems to be advancing.)
In Xurnese, there are a number of postpositions that are derived forms (e.g. dzušši 'since' < 'before and back to'); these likely started as adverbs and occurred after the noun. This helped establish the post-nominal position. The process was likely helped along by the reanalysis of the derivational suffix -iwa as a postposition ga. There would have been a long period when appositions could appear either before or after the noun. Finally a tipping point was reached and only postpositional order was accepted.