This happens literally every single time I book a JetBlue flight with either Etihad or Qatar points. The problem appears to be that the birthdate isn't passed along from the partner to JetBlue's system in a way that it understands. Only solution I've found other than calling JetBlue is to use the ticket number in the JetBlue app to retrieve the reservation without the stupid birthdate error. It seems like after that, you can use the "Manage Trip" button in the app to access the reservation to assign seats and whatever else. Also, if you then add your JetBlue number to the reservation that way, you'll be able to access it normally through the website or anywhere else by just logging in.

Note that the last time I did this, the "Manage Trip" option didn't work immediately even in the app, but it did a few hours later. Not sure if it was just a timing thing or if I needed to log into the JetBlue app, which I did the second time around.