I am thinking of using the new java 8 Date Time API. I googled a bit and found jodaTime as good choice for java but still kind of interested to see how this
Yes, the Java API will take DST changes into account.
This tutorial explains quite well how to convert dates between timezones and how to choose the right class to represent a date: https://docs.oracle.com/javase/tutorial/datetime/iso/timezones.html
You can also look at this class which represents the rules for each zone: http://docs.oracle.com/javase/8/docs/api/java/time/zone/ZoneRules.html
In particular, this method can tell you if a particular instant is in daylight savings: http://docs.oracle.com/javase/8/docs/api/java/time/zone/ZoneRules.html#isDaylightSavings-java.time.Instant-