Environment="USER=ubuntu" "Path=/home/ubuntu/console/bin" 
WorkingDirectory=/home/ubuntu/console/bin
ExecStart=/bin/sh -ec "exec /sbin/start-stop-daemon -S -c ${USER} -d ${Path} --pidfile=/var/run/console.pid --oknodo  --exec consoleExecutable " #2>/dev/null
ExecStop=/bin/sh -ec "exec /sbin/start-stop-daemon -K --quiet -c ${USER} -d ${Path} --pidfile=/var/run/console.pid  --retry=TERM/30/KILL/5 --oknodo --exec consoleExecutable" #2>/dev/null

This is almost worthy of the systemd House of Horror. Were it not the case that there's a horror story already in there that does this.

Do not use start-stop-daemon in a service unit to do all of the things that a service unit already does. With unnecessary PID files and the wrongheaded assumption that ExecStart accepts shell syntax comments, no less.

And do not do what the other answer says and try to bodge it with Type=forking. That makes things worse, not better.

The nonsense with start-stop-daemon is why things are going wrong. Because the process running start-stop-daemon does not become the service, but in fact exits pretty much imediately, systemd is thinking that your service is terminating. In your first systemctl status output, you can see that systemd is in the middle of sending SIGTERM to clean up all left-over running processes after running the ExecStop action, which is what it does when it thinks that a service has terminated.

Just do things simply:

Type=simple
WorkingDirectory=/home/ubuntu/console/bin
User=ubuntu
ExecStart=/home/ubuntu/console/bin/consoleExecutable

No ExecStop nor Environment is actually required.

Further reading

• Jonathan de Boyne Pollard (2015). You really don't need to daemonize. Really.. The systemd House of Horror.
• Jonathan de Boyne Pollard (2016). If you have two services, define two services.. The systemd House of Horror.
• Jonathan de Boyne Pollard (2015). Readiness protocol problems with Unix dæmons. Frequently Given Answers.
• Systemd kills service immediately after start

What you are seeing here is the expected systemd behavior. The Requires= dependency will make sure mysql.service is started whenever tomcat.service starts, but once started the two units are independent and one won't be stopped when the other is.

If you really want mysql.service to be stopped when tomcat.service is, you can use the PartOf= directive which links units on stop and restart.

For the example you described (having mysql.service stop whenever tomcat.service is stopped), what you need is to add PartOf=tomcat.service to the definition of mysql.service. Usually, the best way to do so is to use an override file, which you can do with systemctl edit mysql.service which will open a text editor with an empty file, then you can add this snippet to it:

[Unit]
PartOf=tomcat.service

This will get saved in a file /etc/systemd/system/mysql.service.d/override.conf which becomes part of mysql.service, you can check that with systemctl cat mysql.service.

After those changes and a systemctl daemon-reload, this should work as you expect...

Regarding ordering, everything should work as you expect with the single After=mysql.service you have in tomcat.service, since the dependencies are respected in the reverse order when stopping services. (Which means, in this case, tomcat.service will be stopped first, followed by mysql.service.)

Stopping units this way might not be always a good idea... Perhaps a slightly better approach is to create a separate .target unit to group all services you want to control together. Perhaps something like webservices.target.

You would create that unit with contents such as:

[Unit]
Description=Web Services
Requires=tomcat.service mysql.service
After=tomcat.target mysql.service

[Install]
WantedBy=multi-user.target

And then have both tomcat.service and mysql.service set a PartOf=webservices.target, using the override mechanism described above.

Enable the target unit with systemctl enable webservices.target, and then you can start and stop both services together with systemctl start webservices.target or systemctl stop webservices.target.