When enabling a systemd-service why it isn't started?

Question

When running

systemctl enable my-service

it gets correctly enabled (the link is created into the right WantedBy-target in /etc/systemd/system) but it is not started.

However, when rebooting the machine systemd starts the service.

What do I need to do to have systemd start the service when enabling the service?

For reference, here's my unit-file:

[Unit]
Description=WebSocket-server-application
[Service]
ExecStart=/usr/bin/ws-server.app
Restart=always
[Install]
WantedBy=multi-user.target

(A little bit of background: systemctl enable is called during package-installation. I need to have the service started once the package has been installed.)