I agree with Vaim Caen's answer that this is a timezone issue, but not with parsing - the date is being parsed fine, but into your local timezone, while you're expecting it to be parsed into UTC date.
This answer shows how to convert from your current timezone to UTC - applying this to the TryIt demo gives:
var msec = Date.parse("2013-06-18T12:00:15Z");
// or: var msec = Date.parse("Tue Jun 18 2013 08:00:15 GMT-0400 (EDT)");
var d = new Date(msec);
d.setTime( d.getTime() + d.getTimezoneOffset()*60*1000 );
document.getElementById("demo").innerHTML = d;
Edit: If you all you're interested in is displaying the date (no further manipulations) then you can use:
d.toUTCString()
which will show the date in GMT (for me it actually shows "GMT" so most likely not of use!)
The alternative is to add a function to the prototype to show the date in whatever format you want and use the date.getUTC*
methods.