Normally, you'd enable quotas, though from my testing prior to responding, it doesn't seem that doing that works as it should. I've tested this on Ubuntu 14-16.04 and 16.10, though the errors persist, so what I've done is submit a ticket to DigitalOcean asking them to see if it's possible.
I know that DigitalOcean doesn't allow you to modify the kernel and on the stock kernels that come w/ Ubuntu, quota won't work. To confirm this, I installed the kernel updates as well as the quota package and then used
modprobe where needed. While I could bring up the correct files on each user, it'd fail when saving the changes.
As soon as I hear back from DigitalOcean, I'll update this ticket to confirm whether or not this is indeed possible.