Both are past relationships Ryuki had, though they were fairly different. With Malva, she attended some of his concerts when he was touring in Kalos and was able to meet him backstage thanks to her connections. One thing led to another and the two ended up having a fling that lasted a few weeks. Once Ryuki returned to Alola, however, he and Malva never spoke to each other again, both understanding that their relationship was purely physical and temporary.
What Ryuki didn’t expect was that this fling resulted in him becoming pregnant. He decided to keep the baby and Nasuka was born 9 months later. Ryuki wasn’t about to halt his career just since he had had a baby though, so much of Nasuka’s early life was spent on the road, being looked after by the crew while her dad performed. Eventually, however, Ryuki settled more permanently in Alola, where he opened his Kanto-style Gym.
Some years later, Ryuki and Cross met for the first time when the latter was challenging his “Gym”. They also ended up in a relationship that’s mostly physical, but this time things were a bit more serious and lasted longer. Cross never fully moved in with Ryuki, but he was around pretty frequently which Nasuka didn’t appreciate much, as Cross wasn’t really a fan or her or kids in general. This is also why, when he and Ryuki end up expecting a child together, their relationship kind of collapses. Cross didn’t want a kid at all but Ryuki thought having another brat around would be cute – they weren’t able to compromise, so Ryuki just broke up with him.
That said… once Briar was born, Ryuki was just as hands-off as he had been with Nasuka, which resulted in Nasuka having to half-raise her little brother herself since their father was off working on his music or at his Gym so much. Having to look after her little brother all the time means that Nasuka spends a lot of time at home rather than being able to go out, so she ends up on the internet drawing spicy doujinshi and most of her friends were made online. This is how she ends up meeting Cyril and is significant to his storyline!