This is what I received from Chase serve rep:
Thank you for contacting Chase. The anniversary night for the World of Hyatt credit card will be issued 10 weeks from 01/17, the anniversary date of the credit card. This would put you at receiving your anniversary night 03/28.
Nights are eligible for redemption for one year from the date it is deposited into your World of Hyatt member account. Please be aware that nights cannot be extended or reissued after their expiration.
It is absurd to take 10 weeks to post....