You could use date_default_timezone_set to make all time-related functions acknowledge the shift. First thing to do is to convert those minutes into hours, since the UTC gap is 1 hour between n and n+1.
$hours = $minutes / 60;
I would also recommend that you check the minutes values first :
if($minutes % 60 == 0) // We're good.
Now, if you want to convert the UTC offset to a timezone, you can create your function :
<?php
function offsetToTimezone($offset){
    $timezones = array( 
        "-12" => "Pacific/Kwajalein", 
        "-11" => "Pacific/Samoa", 
        "-10" => "Pacific/Honolulu", 
        "-9" => "America/Juneau", 
        "-8" => "America/Los_Angeles", 
        "-7" => "America/Denver", 
        "-6" => "America/Mexico_City", 
        "-5" => "America/New_York", 
        "-4" => "America/Caracas", 
        "-3.5" => "America/St_Johns", 
        "-3" => "America/Argentina/Buenos_Aires", 
        "-2" => "Atlantic/Azores",
        "-1" => "Atlantic/Azores", 
        "0" => "Europe/London", 
        "1" => "Europe/Paris", 
        "2" => "Europe/Helsinki", 
        "3" => "Europe/Moscow", 
        "3.5" => "Asia/Tehran", 
        "4" => "Asia/Baku", 
        "4.5" => "Asia/Kabul", 
        "5" => "Asia/Karachi", 
        "5.5" => "Asia/Calcutta", 
        "6" => "Asia/Colombo", 
        "7" => "Asia/Bangkok", 
        "8" => "Asia/Singapore", 
        "9" => "Asia/Tokyo", 
        "9.5" => "Australia/Darwin", 
        "10" => "Pacific/Guam", 
        "11" => "Asia/Magadan", 
        "12" => "Asia/Kamchatka" 
    );
    return $timezones[$offset];
}
?>
... and use if for conversion :
date_default_timezone_set(offsetToTimezone($hours));
By the way, I suggest you have a look at this answer, which provides you with a more elegant way to achieve the work of offsetToTimezone.
Now that your script if configured on the correct timezone, just ask for a timestamp :
$timestamp = mktime(0, 0, 0);
If at some time, you need to reset to timezone to default, you might need date_default_timezone_get to save it :
$timezone = date_default_timezone_get();
// Change to another timezone based on your offset.
// Get your timestamp.
date_default_timezone_set($timezone);