Perfect timing for your question: I just checked mine this morning!
We used my wife's card referral to open a new card in my name - approved on May 19th.
Received new card within a week, spent the $500 and paid balance off on June 13th.
(Since new card, First payment wasn't due until July 15th, but we are leaving on our trip on July 25th so I paid off balance on new card immediately to try to get the $200 reward card process moving.)
Checked my wife's rewards today (a week later, few days after monthly credit cycle closed) and the $50 referral was applied to her rewards.
As for my $200 reward, I called last week to ask about both rewards and they told me they would be applied at end of cycle that just closed - I am hoping that since the $50 referral was applied to my wife's acct as they told me, that my rewards card ships soon as well. Think I might call and see if they can verify that.
BTW, As I understand it, the $50 referral should be triggered when the referred person uses the card once, not when they hit the $500 spend to get their own reward. (But that info could use some double checking.)