The Google Assistant can do a lot of things, but apparently, it doesn't know that Arizona is not in the Eastern Timezone. Now this isn't just as simple as changing the timezone that Arizona is associated with, because that State is the only one in the US that does not observe daylight savings time. So during part of the year it's on Mountain Time and the rest of the year it's on Pacific Time. Which is likely why the Google Assistant is confused on the time in Arizona, but it's still a bit strange that it believes Arizona is on the east coast, when it is definitely not.
Now this bug is not happening with other States, it only appears to be happening with Arizona, and given the fact that it doesn't observe Daylight Savings time, that does make sense. It's also happening in Google Search on the desktop, so it's not just Google Assistant that's having the issue. It appears to be a Google Search issue at this time. Google has said that it is working on a fix for this issue, and should have it fixed relatively soon. This is the type of fix that likely won't need a software update either, seeing as it should all be done on the server since it is a Google Search issue and not a simple Google Assistant issue.
Google Assistant has had some interesting bugs since it launched last year, but this is perhaps the most confusing one. Hopefully it's something that Google can fix in the next few days. The Google Assistant is pretty good, but it is a bit fragmented right now. The Google Assistant on Google Home, versus on your smartphone versus what's in Allo is vastly different, surprisingly. Google has added more functionality to Assistant which lives inside of Google Home, and less to what's on your smartphone, which is a bit weird since many more people have a smartphone that has Google Assistant rather than a Google Home – since those are $129, the price of some smartphones these days. You can check out the Google Product Forums for updates on this issue from Google, but there's no ETA for a fix just yet.