Use Collection.sort() and Comparator.comparing(), I find those easy to read when coming back to it later:
data.sort(Comparator.comparing((String[] o) -> o[1]).reversed());
You can compare the timestamp without conversion, as the format is "correctly" ordering the fields.
If you are confined to Java 7, there will be more boilerplate:
Collections.sort(data, new Comparator<String[]>()
{
    @Override
    public int compare(String[] o1, String[] o2)
    {
        return o2[1].compareTo(o1[1]);
        // return -o1[1].compareTo(o2[1]);
    }
});
Note that I need to compare o2 to o1 in this order or negate the result of comparing o1 to o2 to order the data descending. This becomes much more obvious in the first approach.