I just signed up for the Plus and Premier cards at the same time (in two separate browsers) and was instantly approved for both.
I used a referral from Professor Eck for the Plus card but I had my own offer in an email from Southwest for the Premier card. The email specified a 50,000 point bonus and I used the link in the email to the Chase form, however I was slightly dismayed that the Chase form didn't say anything specifically about bonus points. I know it had my data from the email offer because a couple fields were pre-filled already (my name). The email offer did not expire until 10/22 so I should be good there.
The form from Professor Eck's referral had the 50,000 point bonus shown right there. Somehow I'd like to verify that the Premier card I signed up for included the 50,000 point bonus, just to be safe. I have a Chase Online account and I was looking around there (both cards show up) to see if there was anything that mentioned the bonus but I haven't come across anything yet. Does anyone know if that information shows up in your Chase Online account anywhere? I suppose I can call Chase for verification?
Also, I'm having difficultly figuring our when the first statements close. All I see is that the first payment is due by 11/17 and 11/19. If that's accurate then apply now was technically too early because I think they give you 21+ days to make the payment, which would put the first closing dates in October.
EDIT for Update: I called Chase and the lady said my Plus card's first cycle won't close until 11/20 and payment will be due on 12/17. So what I saw on my Chase online account with a due date of 11/17 was actually a phantom due date as if I already had a card. Whew! Just thought I would add that info just in case anyone else signs up, looks at their Chase Online account immediately afterward, and has a little panic attack like I did. :)