When righthander Kirby Yates made the Yankees out of spring training, one of the first people he wanted to call was his big brother, former Mets pitcher Tyler Yates.

First, Kirby had to check the time on his phone. It was six hours earlier where Tyler lives — the Hawaiian island of Kauai, where Tyler is now a police officer.

Tyler, now 38, was the first player who went to high school on Kauai to reach the major leagues when he debuted with six shutout innings against Montreal for the Mets in 2004. Kirby became the second when he made the majors as an undrafted free agent with the Tampa Bay Rays in 2014.

Lefthander Steve Cooke, who was born on Kauai but went to high school in Oregon, pitched for the Pirates and Reds from 1992-98.

The Yankees purchased Kirby’s contract from Cleveland on Jan. 8. The 29-year-old was the last man added to the Opening Day roster and probably would have started the season in Triple-A if Bryan Mitchell hadn’t suffered a broken foot in the last week of spring training.

Tyler Yates Photo Credit: ASSOCIATED PRESS / Eric Gay

Still, Yates the younger is looking like someone who might be here to stay. He has six strikeouts in 3 1⁄3 innings in four appearances, although he has allowed two runs in that span.

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All of which is a pretty big deal in the brothers’ (and Cooke’s) hometown of Lihue (population 6,450), which is best known on the mainland for its destination wedding resorts on picturesque Kalapaki Bay.

“I can’t go anywhere around Kauai without people coming up to me and saying congratulations and how they’re watching Kirby,” Tyler said in a telephone interview. “There’s definitely a lot of support for him over here. When he was traded to the Yankees, I was like, ‘Really? The Yankees?’ When he made the team, I was very excited.”

Kirby was just as excited as a high schooler when Tyler made his first appearance in the majors at Olympic Stadium in Montreal on April 9, 2004.

“I was a freshman or sophomore in high school and my dad owned a bar,” Kirby said. “So I was up there watching it with my dad and about 10 or 12 other people. I only got to watch three innings and then I had to go to practice. I showed up late at practice and my coach was actually [annoyed] at me and made me run laps. I was like, ‘My brother is making his big-league debut. What do you expect?’ ”

Tyler went on to a five-year career with the Mets, Braves and Pirates that was shortened by two Tommy John surgeries. He finished with a 12-17 record and 5.12 ERA in 239 games.

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When his career ended, Tyler went back to Kauai and coached some baseball. He wanted to be a fireman but found a more direct path to employment as a police officer and started on the force in June 2013.

“Me and my dad were like, ‘You sure you want to do this?’ Kirby said. “But his personality and stuff, he kind of fits that mold to be a cop. He doesn’t really take a whole lot of crap.”

Tyler said being a cop on the idyllic-seeming “Garden Island” is busier than people might expect. He said drugs, domestic violence and homelessness are some of the issues he tries to combat on a daily basis.

“Believe it or not, there’s a lot of crime,” he said. “That’s one reason I became a cop. I want to do my part to make the island a safer place for my children.”

Tyler, a father of two, was listed at 6-4 and 220 pounds during his playing days. Kirby is 5-10 and 210 pounds. Kirby spends his offseasons on Kauai and called Tyler his “personal pitching coach.”

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“He throws the ball almost the same way that I do,” Tyler said. “He just never threw as hard as I did. But for a little guy, he throws pretty hard.”

Yankees manager Joe Girardi has praised Kirby for the quality of his stuff. That means a lot to a pitcher who didn’t know what to expect after the Rays sent him to Cleveland in November and the Indians turned around and sent him to the Yankees two months later.

“Honestly, I’m just ecstatic to be back in the big leagues again,” Kirby said. “Especially after the year I had last year (1-0, 7.97 ERA in 20 games). I really didn’t know what to expect or what was coming my way in the offseason. I was expecting it not to be good. The way it all worked out, it couldn’t have worked out any better.”

Kirby got the lowdown on playing in New York from his brother, who went 2-4 with a 6.36 ERA in 21 games in his only season with the Mets in 2004.

“It’s so different from where we’re from,” Kirby said. “It’s so neat, too.”