Ending the application by "closing it" may kill the process, but it may have several services running. I'm on my phone, so I cannot add the references, but having multiple apps in memory isn't that bad- I don't think it really effects the life of your battery.
In this instance, if you think (or know) that a particular application is being a pain, I would suggest you first download the application "Watchdog". This gives detailed information about applications, and then let's you kill them when they become too consuming. Watchdog is very good for analysing the running services. If you do find your application is misbehaving, then you have a problem.
If Watchdog does not mark the application as misbehaving, then we may need to dig deeper. If possible, try to run tasker with an automated script to kill the services of this application, which should in turn kill all instances. Whether this is what you want, or is safe, is another question.
One thing to take into consideration is did the application consume so much when your phone was not rooted? Perhaps SU has removed the restrictions the application once had..