From 12th May 2016, the USCIS would start the premium processing for limit subject H-1B petitions requesting premium processing that includes petitions seeking exemption for individuals with higher or master degree.
USCIS had initially declared in its press release that it will provisionally adjust its practice for premium processing because of historic receipt levels of premium processing, with the possibility that H-1 B limit would be met in the initial 5 working days of the season for filing.
USCIS has offered a service of premium processing for few job based petitions and also guarantees a two week processing time.
Petitions for H-1B which are not subject to limit and for any other classification of visa, the two week period of processing for service of premium processing starts on the date which the USCIS gets the request. For limit subject petitions for H-1B, that includes petition for advanced degree exemption, the two week period of processing would start on 12th May 2016, despite of date on I-797 notice of receipt, that specifies the date on which the premium processing fee has been received.