He took Luke to build his lightsaber after a year of training and fighting. She’d already had a father, even though he was dead now. Luke was catching his drift, but Leia didn’t really care. He continued to train Luke and Leia and started dropping hints that Anakin Skywalker was alive and not what they’d want him to be. He’d had 50 million, alive or dead, right before he’d been pulled to this dimension. He used to have higher bounties back in his universe, thanks to him ruining the Hutt slave trade. Luke has a bounty on his head - 25 million credits, wanted alive, unharmed - and he scoffs. He couldn’t say that out loud though, for the twins wouldn’t believe him and everyone in High Command would think he’s colluding with Vader.
No, not vicious, he just had a purpose now, Luke thought. When Father started making appearances again, everyone agreed something was different. They called him Luke Time, because having two Luke Skywalkers would be too confusing. Not this time.) and told Luke and Leia he was there to train them and that they were twins. Not the one so broken it had taken too long to understand why he was so familiar he could always identify his father half a galaxy away. He does not answer Luke if he knew Anakin Skywalker (he did, of course he did, but not this one. He answers their questions about his motives, reasonings, powers, where he came from, etc. He hadn’t tempted father enough to pull him from his hiding places (he’s not dead, Luke would know if he was dead, he would), so he goes back to the Rebellion to teach Luke and Leia, as well as tell them the truth. One year later, he returns to the Rebellion. He didn’t think they knew each other, or their father, so he’d rather them not find out unless it would be from him. Now, the Rebellion will have less to fight, less chance of them dying, less chance of them meeting with Father prematurely. But what he is doing will help them in their state now.
He wants to teach his other sister how to fight, how to win, and how to see the possibilities and possible consequences of her actions. (is it kidnapping if they’re not a kid? Adultnapping? Hmmm.) He wants to teach his other self, the self that lived in a desert without a Jedi to train him how to fight their father. He is trying to draw his father out of a hole he slunk into so that he could either talk sense into him or kidnap him. So he starts bringing down slavers, freeing slaves, and taking out a few strategic bases for the Empire. (he never thought he’d have to go against his father he does not like this at all) So he stayed with the Rebellion for a little while to get a feel for the world, what they needed, who was there, what would hurt the Empire the most. Apparently, he was in a different universe, one where his father turned to the Dark Side, where his father helped build an Empire, where his father was responsible for enslaving billions of sentients. He had the patience of a 900 year old troll and the discrimination of a former slave. This Jedi was Luke Skywalker, from the 1st story, who was taught primarily by Yoda and Anakin. After a month, they called him Time, for he seemed like a clock counting down to something. So they brainstormed to find a nickname to call him. He pulled her aside later that night and told her that the Jedi felt familiar in the Force but Luke had a hard time placing it. She told Han and Luke and while Han blew it off, Luke looked contemplative. He stared at her for an uncomfortable minute and his facial structure under his hood reminded her of Luke. She was on her way to talk to Mothma about getting a more active role in the field and he was leaving to strike out on his own.
Leia had met this Jedi only once before he left. In the course of a year, he made the Hutts and Zygerians an endangered species, dramatically decreased the presence of slavery in the Outer Rim, and blew up 3 Imperial bases on his own.
He gives Mothma a way to contact him and sets off, not to be seen for a year even though they could track him by the wake of destruction left in his wake. He does not give his name (he likely thinks they know it already), but travels with them for a month until he sees the purpose of the Rebellion.