Not the author of the post, but good question - Typically, the amount is prorated as you inferred or you just kick out to another 12 months, meaning you'd be signed up for 15 months total. I've seen both, but the former is more popular.

The issue comes in how you calculate your SaaS metrics, because the MRR/revenue upgrade is easy enough (prorated over the next 9 or 12 months in your example), but it's tricky when trying to calculate where you attribute the customer upgrade.