About results !!! 
=================

Actual result:
----------------
Kiev:1394781415

New-York:1394781415

UTC:1394781415
==========================
Kiev:1394748000

New-York:1394769600

UTC:1394755200


Expected result:
--------------

Kiev:1394781415

New-York:1394781415

UTC:1394781415
==========================
Kiev:1394755200

New-York:1394755200

UTC:1394755200

I take that to mean the Expected and Actual results in the report were backwards?

Not a bug. "Now" is the same everywhere in the world, thus the same timestamp, but "midnight" most certainly is not.

So strtotime it's function that work with local time zones or with UTC? or with both? It's problem for me because strtotime("now") and strtotime("now GMT") it's have some diff

How i can know when i write some word-params to strtotime() whet it will be UTC and whet it use local time. For example strtotime("next month -1 day")?

<?php
date_default_timezone_set("Europe/Kiev");
echo "Kiev: ".strtotime("now") . " " . strtotime("now UTC");
echo "<br><br>"; 

date_default_timezone_set("America/New_York"); 
echo "New-York: ".strtotime("now") . " " . strtotime("now UTC");
echo "<br><br>";
date_default_timezone_set("UTC"); 
echo "UTC: ".strtotime("now") . " " . strtotime("now UTC");
echo "<br>==========================<br>";

date_default_timezone_set("Europe/Kiev");
echo "Kiev: ".strtotime("midnight") . " " . strtotime("midnight UTC");
echo "<br><br>";

date_default_timezone_set("America/New_York"); 
echo "New-York: ".strtotime("midnight") . " " . strtotime("midnight UTC");
echo "<br><br>";
date_default_timezone_set("UTC"); 
echo "UTC: ". strtotime("midnight") . " " . strtotime("midnight UTC");
echo "<br><br>";
?>

Result:
Kiev: 1394787250 1394794450

New-York: 1394787250 1394772850

UTC: 1394787250 1394787250
==========================
Kiev: 1394748000 1394755200

New-York: 1394769600 1394755200

UTC: 1394755200 1394755200

======================

Comments: Why "now" and  "now UTC" has different values? its a bug!

It will use whatever timezone you provide, or the default if there wasn't one. The question is whether the timezone matters for the string you provide.
"now" is now, like I said. Timezone is irrelevant. "now UTC" will be the current time in your timezone treated as if it were instead a UTC time. "next month -1 day" will be the current date and time, in the current timezone, in one day less than a month from now.

There is documentation specifically dedicated to this question.
http://www.php.net/manual/en/datetime.formats.php
If that doesn't answer your question about a format, simply try it and see what happens.