Now, about Trim... Trim is only an advisory command. You tell the disk, "I'm not using these LBAs anymore, so feel free to do whatever with them." The disk has the option to completely ignore your Trim command, and even if it does mark those LBAs as unused in whatever LBA->NAND mapping table it uses internally, the disk can also continue returning the old data on reads of those LBAs if it wants to. There are disks that make the guarantee that Trim'd LBAs will always read back zeroes until written again (an ATA feature called Read Zero After Trim), but I'm guessing DigitalOcean isn't using SSDs that support RZAT since that's generally only found on more expensive SSDs, like Intel's DC S3700.
What I'm getting at is that Trim isn't guaranteed to do what you think it does. Unless the disk supports RZAT, the only way you can guarantee that the disk won't return old data in response to a read command is to write zeroes over that block.
If you're a VM provider and can't count on Trim doing what you want it to (reading back zeroes on Trim'd LBAs) because your drives don't support RZAT and you don't want zero out partitions at creation or destruction time, the right thing to do is encrypt every partition with its own randomly generated key at creation, then destroy the key when the partition is destroyed. Users will see random data soup on their shiny new block devices, which isn't as nice as seeing a zeroed out block device but is still nicer than seeing some other user's raw data. (Also note that doing this doesn't stop you from also issuing a Trim for a partition when destroying it so the SSD gains some breathing room.)