I think the major issue with your question (both its original form and the edited one) is that you have two questions mixed in one:
How to convince [someone] to contribute to back to the open source community?
This is a general question which applies to any company. The only (somehow) relevant context info is that a company uses open source software.
WTF is the reaction I received from my manager, since I did nothing wrong?
This is a specific question which concerns your particular case. Here, the context matters: what you did exactly to contribute to open source community, and how your company was mentioned.
My answer, if you've read it, replies exactly to this second question, explaining the reaction of your manager, and why you may indeed be subjected to disciplinary action—because you do your personal stuff during your work hours. This is essentially the situation which led you to ask the question in the first place.
Notice that Snowman's answer is also bound to the context. His answer is, IMHO, plainly wrong (sorry; nothing personal), because it misses the point that your tutorials made no reference to the company, but still attempts to explain the reaction of your manager in your specific case. If your tutorial was published as being written by an employee of Example Corp. instead of a named person (for instance, on a public corporate blog or documentation website or simply containing the name of the company), Snowman's answer would be right, and mine—wrong.
On the other hand, the way you formulated your question may also lead to context-agnostic answers, that is to explain how an abstract person working in an abstract company should convince an abstract manager to contribute to open source community—and the title of your question is exactly that. It's a perfectly valid question, except that the context you provide in the question is then completely irrelevant and makes it impossible to answer this context-agnostic answer.
In my opinion, you should split this question in two:
The first one will explain that you were contributing to open source community by writing a tutorial during your work hours, but your manager is angry and you don't understand why, since you believe that you did nothing wrong. By the way, you haven't mentioned the company anywhere in this tutorial, so it doesn't affect your company's PR. Why is your manager screaming at you? (My answer replies to that) Would it be better to mention the company in the tutorial? (Snowman's answer replies to that)
The second one explains simply that your company uses a lot of open source content, and you consider it fair to contribute back to open source community. How should you convince your management to do it?
