Hyatt's online booking engine is not compliant with certain EU electronic payment regulations, so the property is not able to use the card you attached to the reservation. This kind of request is legitimate and not a phishing attempt. Note that your reservation will be cancelled if you do not make payment as requested.
If you plan to use a Hyatt credit card on a third party site, buyer beware.
I encountered a third party payment site in connection with a stay at a Hyatt in Greece last year. Although I charged the stay to my Hyatt credit card, I did not receive points for doing so because Hyatt's system (understandably) did not recognize the third party site as having anything to do with Hyatt.
After a lengthy (couple of months) back-and-forth with Hyatt, I eventually got the points but it was a hassle I didn't need.