How does one instruct Pulumi to execute one or more commands on a remote host?
The equivalent Terraform command is remote-exec.
Pulumi currently doesn't support remote-exec-like provisioners but they are on the roadmap (see https://github.com/pulumi/pulumi/issues/1691).
For now, I'd recommend using the cloud-init userdata functionality of the various providers as in this AWS EC2 example.