Here's what's going on, according to www.irs.gov:
If you had your filing fee taken directly from your refund or you got a rapid refund/anticipation loan, you will be getting a check in the mail. If you paid your filing fee ahead of time you will be getting your stimulus by direct deposit into the same bank account your tax refund went into.
When exactly you get your rebate/stimulus depends on the last two numbers of your social security number. If it's a joint return, it's based on the social security number listed first on your return. For example, my husband's name is listed first on our joint return, and his last two numbers are 99. We had our filing fee taken out of our refund, so we probably won't be getting our stimulus payment check until mid July.
I recieved the same letter in the mail that you did regarding the payment date. Mine also said May 16th, though the letter was dated May 19th. It also said that if you haven't recieved your stimulus by six weeks from the date on the letter to contact the IRS.
Hope this helps!