The main problem is that your closing figure tag is forgotten with you. Because of this subtitle problem the mentioned site to generate outline, consider all the next elements after figure element as subset of figure element.
It means figure element becomes their conteiner. Now, due to this deduction by that site all of the contents of your document after figure element condider as a content of a Sectioning Root element (blockquote, body, details, dialog, fieldset, figure). As I am sure you know the sections and headings inside these elements do not contribute to the outlines of their ancestors. Headings in a Sectioning Root element will not be included in the main document outline. That means you can have a complex heading hierarchy within a blockquote without worrying how it will affect the overall structure of the document.
To make sure about this answer, please test following html snippet, you will see the same result:
<body>
<nav>
<h1>Navigation</h1>
<ul>
<li>...</li>
</ul>
</nav>
<h1>My fantastic site</h1>
<figure>
<img src="" alt="" />
<h2>About me</h2>
<p>I am a man who lives a fascinating life. Oh the stories I could tell you...</p>
<h2>What I do for a living</h2>
<p>I sell enterprise-managed ant farms.</p>
<h1>Contact</h1>
<p>Shout my name and I will come to you.</p>
</figure>
</body>
but I think this is what you whanted:
<body>
<nav>
<h1>Navigation</h1>
<ul>
<li>...</li>
</ul>
</nav>
<h1>My fantastic site</h1>
<figure>
<img src="" alt="" />
</figure>
<h2>About me</h2>
<p>I am a man who lives a fascinating life. Oh the stories I could tell you...</p>
<h2>What I do for a living</h2>
<p>I sell enterprise-managed ant farms.</p>
<h1>Contact</h1>
<p>Shout my name and I will come to you.</p>
</body>