I can't reproduce the issue here as you can see on this screenshot (SEF off)

(SEF on )

@infograf768 if you have SEF off please make sure that the Year and Month filter is set in the view.

For me it is not see:

It allways only apply the month filter ;)

in your example above, the year is not stated, only the month. As both articles were published in October, they both show.

1. To display the articles dates below the article title, I modified an archives menu item parameters to do such (but, if I do not have such a menu item, default would be global)
2. Not using that menu item, I click on an archived article in the module url obtained is: http://localhost:8888/trunkgitnew/index.php?option=com_content&view=archive&year=2015&month=3&Itemid=256 => the result displays with the filter set to the article month and year, i.e here March 2015

3. I then change the month in the filter to Month and switch the year to 2014 in my example. I click on the filter Button. I get this url:
   http://localhost:8888/trunkgitnew/index.php?option=com_content&view=archive&Itemid=256
   the correct article is displayed:
   

4. If I change the filter to Month and Year then click on the Filter button, I get the same url and it displays correctly both articles as both Month and Year are not specified:

The date used for filtering is the 'Published Date`.

No bug here. Works fine.

No bug here. Works fine.

Yes the filter generally work. But the SEF URLs that was created by the archive module is wrong. If i disable SEF all works ok

All works OK when sef is on or off, but, when sef on, after Clicking on the Filter Button, if we have no menu item to Archives Articles, we may get an url of the type: http://localhost:8888/trunkgitnew/component/content/
No effect on display though.

Confirm problem described by @zero-24 that the year filter is not set after clicking on a link generated by the archive module.