Your approach to using Terraform for provisioning infrastructure and Ansible for config management is the right way to think about it. Luckily Terraform should be able to do what you’d like. Pre-formatted volumes created via the API will be automatically mounted to the Droplet. So the key thing is to specify the initial_filesystem_type when creating the volume with Terraform. For example, using this config:

resource "digitalocean_droplet" "foo" {
  name       = "foo"
  size       = "s-1vcpu-1gb"
  image      = "ubuntu-18-04-x64"
  region     = "nyc1"
}

resource "digitalocean_volume" "bar" {
  region                  = "nyc1"
  name                    = "bar"
  size                    = 100
  initial_filesystem_type = "ext4"
  description             = "an example volume"
}

resource "digitalocean_volume_attachment" "foobar" {
  droplet_id = "${digitalocean_droplet.foo.id}"
  volume_id  = "${digitalocean_volume.bar.id}"
}

The resulting volume will be mounted and available at /mnt/bar/ on the Droplet.

If you do not specify the initial_filesystem_type the volume will appear as a raw block device that must be manually formatted and mounted.