I'm suspecting that perhaps the application in question has the KILL_BACKGROUND_PROCESSES
permission and uses the killBackgroundProcesses method.
In Android 2, killing processes was kind of occasionally justifiable, but on Android 4 and up, this really isn't something you should be doing to other running applications. I had a task killer app installed on my Nexus One but have had no cause to use one on any post-Gingerbread device.
As far as "fast reboot" goes, I've noticed that some Android versions take much longer to shutdown and start up than others. Cyanogen is super-quick, vanilla Android is only a bit slower, but I always found Samsung's Touchwiz-encumbered Android to be fairly slow on my S3. Fundamentally, if processes need to be shut down cleanly, and there are more of them, then both the shutdown and startup times will be extended. Not really something an application could influence in a reliable fashion.
And don't forget that killing a process (or force stopping in settings) can corrupt that application's data.