Why date field is picking the user's timezone?
In Drupal, dates stored in the DB do not have any timezone fixed to them; it presumes all date fields are consistent in timezone and relies on the system's timezone setting to offset everything to its correct date for displaying. 

There are two different offset settings: the field's timezone settings (which adjust from user's timezone input to the site's timezone) &amp; the user's timezone setting which adjust display from the site's timezone to the user's timezone.

Needless to say, the various offset settings can make for a confusing situation to adjust to your needs. 

If you want to keep the field adjusted to the site's settings and have the users still adjust for their own time zone, you should customize the display of your field so the time zone is presented in an unambiguous format.