Why does iMessage still work when it's closed?

I'm turning off my iPhone and closing iMessage for a reason. I don't want to be disturbed. Yet, messages still come through on my computer even though everything is turned off. So annoying! Is there any way to set this up so when my phone is off, or at least when iMessage is closed that I don't get notified?

I'm using Yosemite. iPhone 6.

Thanks!

I'm not at my MBP right now, but on the iPhone, Settings, Messages, Send & Receive it lists all addresses used to get the text to you. You can eliminate any you don't want it to use. I think the same list is shown under preferences in Messages on Yosemite. If you want silence, turn down or mute the sound. If it's the visual cues, I think there are settings in Yosemite System Preferences to shut down notifications, too.

One way is to open Preferences and uncheck this box...
In each account.
Messages runs a daemon in the background which is why you still get messages.
When you want your messages back, go back and check the box again.

Thanks so much. I'll give this a shot!

There is also a simpler "Do Not Disturb" mode you can turn on on your Mac (or set for certain hours) so that calls and messages are ignored except under certain circumstances. Do a search on "Mac Do Not Disturb" and you'll probably find out more about it.

You can also simply turn off notifications entirely for certain applications from system preferences -> Notifications.