Sent my application in December 8 - they didn't process it until January 10, so I got the purple sticker. So, if you sent in your application near or after 1/1/2019, you'll get the purple sticker.
The check wasn't cashed until January 14 - and I received the stickers about a week after that. So far as I can tell, the transaction of the check is the only real indicator of the progress in processing your application, but once that goes through you're basically just waiting for the mail.