How should I react to an email saying my Apple password has changed?
We can't tell if it's a phishing email or not because you didn't supply any info about it. It's probably phishing because it often is. 

To be safe, just go to Apple's ID Reset page on a device you trust and reset your password. This is especially urgent if you used your AppleID password at another service that was compromised, or it’s easy to guess - one of the 1,000 most common passwords like 123456.

If you're allowed to complete the reset then you know the emails, both of them, were fake. 

If you can't do the reset, you'll have to contact Apple Support ASAP. In no circumstances should you click the links directly in the emails since if they're fake, the web sites you click on will harvest your actual password and you will have given up access to your account. If they are real, you will have the best chance to undo the change that was made by following Apple’s recovery from navigating to Apple pages directly:


https://appleid.apple.com/


Here’s an explanation how to trace a mail and find out if it’s legitimate with images in case that helps:


Is this a legitimate email address from Apple support?