One thing I found systemd really confusing was its treatment of ExecStop in a service script. ExecStart is the command to run when systemd starts the service at system boot up (or when a user tells systemd to start the service). However, ExecStop is run when the starting command has finished running. You have to set RemainAfterExit=yes to have the desired function of running the stop command on system shutdown or on user stopping the service. ExecStop is basically the "on-cleanup" event rather than "to-shutdown-the-service" event.
It is important to keep in mind that systemd is tailored towards daemons. So if your service just runs a command that eventually exits, you need to explicitly tell systemd to treat it differently than a daemon.
Edit: As others noted, you’re probably looking for oneshot + RemainAfterExit.