Here's AgileBits support's response.
On May 9, 2016, at 11:03 PM, AgileBits Support <support@agilebits.com> wrote:
Hi Steven,
Thank you for taking the time to contact us. This screen is 1Password prompting you to enter your new Apple ID and password so it can sync using iCloud. This should open in your default browser. You will see this screen if you have changed this account so can you go ahead and enter that new information.
Please let me know if you have any further questions and I will be happy to help more.
Regards,
Laura Rooke
AgileBits Support Shaker
Here's what I wrote back to them...
Thanks Laura. Your developers should know that the way this “prompt” behavior is very troubling. If I ignored the screen (which I did because I was concerned that it was a type of malware), your program began to regularly open new tabs calling the same sign-in. It literally opened dozens of copies of the same screen overwhelming my browser (first Firefox and later Safari). If I shut down my default browser and tried working on another program on my computer (such as Mail), it would automatically open the browser and begin the same process. I could not work using my computer because of the constant interruptions. Finally, I had to delete both Firefox and Safari to stop the problem!
I strongly recommend you turn off this behavior and instead send an email notification to users prompting them to go into 1Password itself to reset the password.