CVS Pharmacy in Texas also does an auto schedule of the 2nd dose. When I signed up, I got 2 appointments. First dose, then 2nd dose exactly 3 weeks later, same time, same place.
For me, it worked just fine. My company is not interfering in the vaccine process in any way. You get your appointment, you tell us when it is. You get paid time to go get the shot. You don't have to make up time or use PTO. We just request that you try to get a time outside of work hours, or try to minimize your time out of office. If you have a reaction to your 2nd shot, you can take off the rest of the day to recover. My department is a call center, so this is a HUGE concession to have people OOO without any scheduling, but the company does not want to make this thing any harder than it already is.