The Athletics’ left fielder arrived at spring training in the desert Sunday at ease, determined to build on a strong rookie season for the AL West champions.

Cespedes, the 27-year-old Cuban defector, also discussed how late last season he worried constantly about the safety of his family members in the Dominican Republic. He wasn’t sure whether they might be targeted because of his legal issues stemming from a former agent who claims the outfielder owes him money, he revealed to the San Francisco Chronicle late last month. His mother is now safe elsewhere.

“It weighed on my mind sometimes, yes. I tried to be focused every single day and not let it be a problem and keep me from playing baseball hard,” Cespedes said Sunday. “I’m thankful this all was possible because that was a distraction for me but not too much. I tried to put that to the side and not take it with me onto the field.”

Manager Bob Melvin credited Cespedes for his seamless transition to a new country, a new level of baseball and all of the changes that come with both.

Melvin was aware of Cespedes’ personal situation down the stretch and wanted to give him a break, except Cespedes wouldn’t go for it. He predicted at the start the A’s would make the playoffs in 2012, and they rallied over the final 10 games to stun the Texas Rangers on the regular season’s final day to capture the AL West.

“He was very communicative with me as well, so I knew what was going on with him,” Melvin said before Sunday’s workout. “He wears his heart on his sleeve, and when he comes to the ballpark it was pretty easy to see what kind of mood he was in that particular day, but he always found a way to go out on the field and perform. Any time your family situation’s involved and you’re not with them and going through. … It was very difficult for him. There were days I was going to give him the day off but he refused. He wanted to play, so he’s a tough makeup kid on top of it.”

Cespedes told the Chronicle he hopes to soon have a visit from his 3-year-old son, Yoenis Jr., thanks to new laws in Cuba that allow citizens to travel and return. They have been separated since he left his homeland.

Cespedes also said that former agent Edgar Mercedes claimed the slugger owes him 17 percent of his contract, including last year’s $5 million signing bonus, for work Mercedes did to help get Cespedes and his family from Cuba to the Dominican Republic.

Cespedes batted .292 with 23 home runs and 82 RBIs in 129 games, finishing runner-up to the Los Angeles Angels’ Mike Trout for AL Rookie of the Year. He also hit 25 doubles and five triples while striking out 102 times.

At various points during the season, he had to deal with an injured left hamstring, a troublesome left hand that put him on the disabled list and a bone bruise in his right foot in the final weeks.

The foot injury cleared itself up in a few weeks after the A’s lost to Detroit in Game 5 of their division series.

“I feel very good, comfortable and happy at the same time,” Cespedes said. “I won’t do anything different, except for better stretching for my body to be healthy for a full season.”

Cespedes would rather not play at designated hitter, though he understands there will be days his body might need a rest. He’ll play anywhere else Melvin asks, joking he’d even crouch and catch.

“I appreciate the fact that he’s taking that attitude, and I love that,” Melvin said. “We want all our guys to want to play and be out there on the field. We did see last year, it was the first time he played 162 games, and we did DH him some, especially at the end to try to combat that. He plays awfully hard, it’s not like he goes out there and paces himself. He is a little more familiar with the 162-game season, but if I can rest him on a particular day and not have to give him a full day off, DH is probably the best option for that. We’ll see how that goes. I love the attitude.”

As for Reddick’s unkempt look, Cespedes cracked: “I don’t like it. Everybody has different things they like.”

Reddick’s response, “He’s just mad that he can’t grow it.”