Skype showing me as online - after stopping app and even after device shutdown?

Scenario A:

1. start Skype


2. do some other work


3. shut down the Android device

Problem:
My contacts are still seeing me as being "online".
Strangely enough there seems to be no heartbeat feature implemented in Skype.
So even after 1 day my contacts are trying to call me - even though the device is powered off.

Initially I thought this symptom would occur in case i forgot to manually quit the Skype app before shutting down the device.
So i was searching for an answer how to configure Skype to automatically log off / quit when the Android device is shutting down?

But now it turned out the situation is even worse:

Scenario B:

1. start Skype


2. do some other work


3. quit the Skype app


4. shut down the Android device

After step 3 I'm still listed as being "online".
When a contact sends me a chat message it pops up.
So it means: even though Skype no longer appears in the task manager it seems to be running as a secret, invisible background task!?

And after step 4 the behaviour is the same as in Scenario A. I'm not transitioning to "offline" state.

Summary:

There seem to be 3 problems:

• no heartbeat feature implemented in Skype


• quitting the Skype app is not properly terminating / signing off


• shutting down the Android device also is not influencing the online status

The only thing that works for me so far:
You must switch to Skype, tap on your profile, at the very bottom manually do "sign out".
That's just not bearable.

This is:

Android 4.1.2
Skype 4.9.0.45564
Skype 5.0.0.49715
Skype 5.1.0.56619
Skype 5.1.0.58677
Skype 5.4.0.5871 (at least I'm now showing as being "Away" - instead of "Online")

2015-08-15 - the problem is back and it's even worse:
Android 5.1.1
Skype 5.9.0.14047
Even though I'm manually signing out, terminating the app and shutting down the Android device I'm still being shown as being "online"!!

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All of the above tested @ Samsung Galaxy Tab 2 7.0 (WiFi only) / GT-P3110