Went out to see my future home today. The factory actually builds each apartment as a set of modules (or a single module, in my case) and assembles them on location. I'm not allowed on site until all the work has been complete, but the idea is that inside, my little half-bedroom apartment is already painted, with the kitchenette assembled. They'll be putting on the outer panelling and hooking up the utlities, installing home appliances etc. until June.
I'm actually very happy that they are doing the full-surface siding - it's the fourth house of this development (in an eventual set of Seven Dwarves), and the first three just have white plastic on the first two floors. This should look much cooler when it's done.
Kodumaja, the company that makes these, is a Tartu operation, although most of their business is in Scandinavia. So far my experience with them has been quite positive.