Does markdown inside of HTML tags needs two LF after >

Spec
1

Running cmark --unsafe on

<details>
<summary>Info</summary>
* a
* b
</details>

<details>
<summary>Info</summary>

* a
* b
</details>

<div>
> This is blockquote
</div>

<div>

> This is blockquote
</div>

produces

<details>
<summary>Info</summary>
* a
* b
</details>
<details>
<summary>Info</summary>
<ul>
<li>a</li>
<li>b</li>
</ul>
</details>
<div>
> This is blockquote
</div>
<div>
<blockquote>
<p>This is blockquote</p>
</blockquote>
</div>
2

For many HTML tags, yes. See the specification of HTML blocks and specifically the start condition 6 and its respective end condition.