The one city on your list that is ahead of India
New Zealand moves to daylight time on the last Sunday in September and back on the first Sunday in April. From October to early April, Auckland is seven and a half hours ahead of India; through the southern winter, six and a half.
So an Auckland working day of 09:00 to 17:00 in summer runs from 01:30 to 09:30 IST. Updates meant to greet a buyer at the start of the day leave India late the previous evening, and replies sent from Auckland after lunch are waiting when your team arrives. Scheduled sends do this without anyone staying up.
The overlap is short and early: your first hour in the office is Auckland's last. Use it to clear the inbox rather than to start a campaign. InfiQ's own support team works India time, in English and Hindi.