Confirmed; see bottom section, below.

However, please refer to [*Provide a way to retrieve questions and answers that have been deleted*][1] -- which is "status-planned".  
This is a ***feature***, not a bug. And this kind of feature has been requested many times. So, shush please, don't ruin it for us. ;)


----------

----------
Confirmation info:
------------------

You can see this behavior (for now) with this API search: [/2.2/questions?fromdate=1466553600&...][2]

Which still includes the deleted question that the OP references:

    {
      "tags": [
        "java",
        "c#",
        "quartz-scheduler"
      ],
      "owner": {
        "display_name": "Kumar"
      },
      "question_id": 37987057,
      "title": "Need a api or widget like Outlook calendar to create Appoitments"
      ...

According to:

 - [Enable searching with deleted:1 for 10k users][3]
 - [10K+ users can \[still\] search any user's deleted content][4]

This behavior should not be allowed as the API doesn't know that I'm 10K (I'm not authenticated), and I certainly don't own the question.

Also, as a 10K user, I see:

> Note: only content you own is returned when searching for deleted content

When using normal site search for deleted content.


  [1]: http://stackapps.com/questions/1917/provide-a-way-to-retrieve-questions-and-answers-that-have-been-deleted
  [2]: https://api.stackexchange.com/docs/questions#fromdate=2016-06-22&todate=2016-06-24&order=desc&sort=activity&tagged=quartz-scheduler%3Bjava&filter=!)EhwvzgXKKsFs376LZp*)y7pMQF4ZMkg9yqlxI1lLkVzxI8uT&site=stackoverflow&run=true
  [3]: http://meta.stackexchange.com/questions/145060/enable-searching-with-deleted1-for-10k-users
  [4]: http://meta.stackexchange.com/questions/271062/10k-users-can-still-search-any-users-deleted-content