Java util dateformat milliseconds for some timezones don't seem to be correct

From what I understand, java.util.Date stores date as milliseconds from Jan 1, 1970, 00:00...

So, I've tried this code below:

public void testDateFormatBehavior()
{
    DateFormat dfNoDay = new SimpleDateFormat(
            "MMM d H:m:s zzz yyyy"
            );
    // This one should be correct as IST = GMT+5.30
    String expStrDateBegIST1 = "Jan 01 05:30:01 IST 1970";
    // Instead, this one seems to do the conversion to
    // Jan 01 00:00:00 GMT 1970
    String expStrDateBegIST2 = "Jan 01 02:00:01 IST 1970";
    String expStrDateBegUTC = "Jan 01 00:00:01 GMT 1970";
    String expStrDateBegCET = "Jan 01 01:00:00 CET 1970";
    // Should convert to Jan 01 06:00:00 GMT 1970 as CST = GMT-6
    String expStrDateBegCST = "Jan 01 00:00:00 CST 1970"; 
    // This is EST, which is GMT+6... 
    String expStrDateBegEST = "Jan 01 10:00:00 EST 1970"; 
    try {
        Date dBegIST1 = dfNoDay.parse(expStrDateBegIST1);
        Date dBegIST2 = dfNoDay.parse(expStrDateBegIST2);
        Date dBegUTC = dfNoDay.parse(expStrDateBegUTC);
        Date dBegCET = dfNoDay.parse(expStrDateBegCET);
        Date dBegCST = dfNoDay.parse(expStrDateBegCST);
        Date dBegEST = dfNoDay.parse(expStrDateBegEST);
        System.out.println("IST1 milliseconds: " + dBegIST1.getTime());
        System.out.println("IST2 milliseconds: " + dBegIST2.getTime());
        System.out.println("UTC milliseconds: " + dBegUTC.getTime());
        System.out.println("CET milliseconds: " + dBegCET.getTime());
        System.out.println("CST milliseconds: " + dBegCST.getTime());
        System.out.println("EST milliseconds: " + dBegEST.getTime());
    } catch (ParseException e) {
        // TODO Auto-generated catch block
        e.printStackTrace();
    }
}

The output:

IST1 milliseconds: 12601000
IST2 milliseconds: 1000
UTC milliseconds: 1000
CET milliseconds: 0
CST milliseconds: 21600000
EST milliseconds: 0

UTC milliseconds line is correct as we specified 00:00:01 seconds starting from Jan 1 1970. CET is correct. CST is correct as that amount of milliseconds is 6 hours after Jan 1 1970.

However, IST conversion is weird.

http://wwp.greenwichmeantime.com/to/ist/to-gmt/index.htm

IST seems to be GMT + 5:30. In my Java code, it thinks it is GMT + 2:00 instead.

Also, EST is incorrect. It thinks EST is GMT+10:00, not GMT+6:00. GMT+10:00 is AEST, not EST. http://wwp.greenwichmeantime.com/time-zone/australia/time-zones/eastern-standard-time/

Is there something I'm doing wrong?