"It was absolutely insane," Ellis raved to ET's Rachel Smith as the pair met up in Times Square to check out the new Maverick billboards and surprise some lucky fans with tickets to the film.
"They tell you all these [rules of etiquette] like, all these things that you have to do," he shared of meeting the Duke and Duchess of Cambridge. "They speak to you first, you reach out your hand... 'Your royal highness, nice to meet you."
"And then the first question you ask is like, 'So, um, how are you?'" he continued with a laugh. "No one knew what to say. It was crazy -- what do you ask them?"
Thinking fast, Ellis recalled that he asked Prince William about the types of aircraft he'd flown in his time with the Royal Air Force. And while he didn't have much in common with the royal there, he fared a bit better than some of his co-stars.
"Miles Teller, at one point goes, 'Your eyes are so blue,'" he joked. "We were all just completely thrown off... You're a prince! I'm just, I've seen you on TV forever, I don't know, this is crazy."
The film tasks Cruise's character with training a group of elite young fighter pilots to take on a near-impossible mission behind enemy lines, and Ellis said that the A-list action star was a charismatic and thoughtful leader on set as well.
"He was so hyper-focused on each one of us in every single thing we did, whether it was our flights, whether it was, you know, while we were on the ground shooting stuff in the hanger," he shared. "The amount of detail and dedication -- and he gets up with a smile every single day. That was also really cool to see, someone at his level, just happy to do it. It was a lot of fun and inspiring. Super inspiring."
"We would be there hours after we wrapped, and he would still be sitting there telling us stories and people just throwing out questions," he recalled of his time on set. "It was amazing... I was very fortunate for the experience."
Ellis has a special connection to the military -- his father was an Air Force pilot -- and he said it was a "dream" to be able to represent the men and women in the military through the film. Maverick went as realistic as possible, with Cruise putting his young co-stars through a grueling training regimen to prepare for the film's high-flying scenes.
"This whole thing was about discipline and detail," Ellis shared. "Not only did we have to be so specific in portraying pilots, but we also then got up in the air. We obviously had to film in jets, so we're talking about a very serious situation. We had to go through safety protocols three or four times a day."
"You really start to see how Tom builds his movies, and also why they are so good and there's rarely any incidents," the actor marveled. "It's all about everyone, every single day, giving their all -- dedicated, focused into making the film. That, to me, was the biggest thing I walked away with."
Top Gun: Maverick is in theaters on May 27. See more on the cast in the video below.