This is the expected behavior. The first button the customer should see should be the "Buy Now" button. Then, once their registration or log in is complete, they should see the "Purchase" button. You can change the label of the "Purchase" button in the Stripe settings, Exchange > Add-ons > Stripe settings. So, you can change "Purchase" to something like "Pay with Credit Card" if that makes the next step seem more obvious.
That would help a lot -- I'll do it. Thank you.
Also Stripe-Add-on-related, I think: I would really like to be able to add a line of text to the Registration screen at the top. I would also really like to add a line of text to the screen that appears after they submit their registration info. Is there possibly a reasonable way to do either of these things?
Most definitely, I will post that question there, and will send a URL by private message.
Thanks very much,