TAMPA — The last time Gerrit Cole and Josh Donaldson crossed paths, they were engaged in a public battle after Donaldson made the Yankees’ ace the poster child for MLB’s crackdown on pitchers using illegal foreign substances last summer.

So of all the players general manager Brian Cashman could have traded for to upgrade the roster, Donaldson would have seemed an unlikely candidate.

But that’s just what Cashman did on Sunday night — but not before notifying Cole.

“Because of how the public side of this thing played out last year … I owed him that phone call,’’ Cashman said Monday. “I just explained, obviously, ‘We’ve got a transaction that’s going to solve a lot of areas of need, but not sure where this other aspect sits. If it is an issue, it’s something we’ll have to work through.’ He’s like, ‘I’ll be fine.’ He was excited about the opportunity to upgrade in a lot of areas.”

One of the next calls was from Donaldson to Aaron Boone, since he wanted to clear the air with Cole, if necessary. And that’s what the two of them did Monday after Donaldson arrived at Yankee camp following the blockbuster trade that sent Gary Sanchez and Gio Urshela to the Twins, and shortstop Isiah Kiner-Falefa and backup catcher Ben Rortvedt to the Yankees.

“It’s not all that uncommon for [Cashman] to fill me in on stuff before it hits the wire,’’ Cole said. “There’s probably a little extra reason why he reached out specifically [Sunday] night. Look, if you’re committed to winning a championship, this kind of stuff doesn’t matter.”

Donaldson told Boone he wanted to speak with both of them on Monday after his arrival.

“The three of us sat in my office for a while,’’ Boone said. “We had a frank dialogue. … I think it already is buried and a non-issue — not to say it wasn’t a real issue last year for us. I feel really good about those two guys.”

Cole called it a “good conversation.”

“I think he has an edge that’s special and fun to watch, and if you’re on his team, you very much appreciate it,’’ Cole said. “On the other side of the field, it’s something you have to overcome.”

Of the dispute, Cole said, “Where my feet are today, it’s in the rearview mirror.”

Donaldson said he believed the talk was necessary “because, obviously, there was a big stink that was made of it last year. A lot of conversation went on about it. Both sides wanted to meet and address the issue at hand, as far as just hearing one another and ultimately leading us back to our goals. Our goal is to win. Both of us are in the same clubhouse now and that’s what we’re gonna do.”

And he insisted the issue was closed for him once the MLB crackdown began.

“First off, when I named Gerrit Cole as part of the thing, I said, ‘Look, he’s the first guy that’s pitched since [minor league] suspensions had been handed down,’ ” Donaldson said. “That was what I said about Gerrit Cole. I said I thought this was a league problem. I feel like the league has addressed the issues that were at hand. After that, you didn’t hear from me. Today, we’re sitting here and our goal is to win a championship with the New York Yankees.”

Cashman pointed to the Yankees’ acquisition of Roger Clemens from Toronto in 1999 as an example of a “hated” opponent who ended up being a valuable teammate in The Bronx.

When that anecdote was relayed to Donaldson, he bristled at the notion that he’s hated.

While Donaldson and his $50 million owed over two seasons is the biggest part of the trade, Cashman said he made the move because of the various holes he felt it addressed.

He called it an upgrade offensively at third base and defensively at shortstop, since now the Yankees can keep Gleyber Torres at second base and avoid playing Urshela out of position at short.

The arrival of Rortvedt, according to Cashman, brings better defense behind the plate, although he’s played in just 39 games in the majors.

“I think the overall feel for us is that it settled a lot of interests on our end with one transaction, with one particular team,” Cashman said. “It solved a lot of areas of focus that we have targeted.”

The GM also noted that the Yankees didn’t give up any prospects.

“We have a lot of people asking about a lot of guys from our system, understandably so,’’ Cashman said.

Although it remains to be seen what Cashman will do with those prospects, since another potential Yankee target, Oakland first baseman Matt Olson, was traded to the Braves on Monday — as Atlanta somewhat stunningly moved on from free agent Freddie Freeman.

The Yankees will continue to look into the first-base market and could bring back Anthony Rizzo, another free agent.

And they’ve shown interest in some of Oakland’s starting pitching, with the A’s in fire-sale mode.

But this was the Yankees’ first big swing of the offseason.