From what I can tell they aren’t automatically upgraded, and the prices aren’t cut to match. However, it looks like you can upgrade them manually. I believe what you’d need to do is power off your Droplet, select Resize in the control panel (Disk, CPU, and RAM), and then select the new plan on the same $10/month pricing you’re on now but with the updated specs. That should bring your Droplet up to date.

https://www.digitalocean.com/community/tutorials/new-droplet-plans-frequently-asked-questions

Details in the FAQ. I’d certainly do a snapshot first.