To my understanding ... the reason for the April 15th deadline is due to the need for certainty associated with federal training grants/fellowship etc... but if the funding source is from the professor's own research grant, the offer can come anytime... especially if the professor's grant has dried up and is waiting for a new grant to be approved before being able to bring in a student.... Jun/Jul is the time when the results of the new grant would be known. Please correct me if I'm wrong. Well in this case, the professor might not take in any students at all!