Su cuy'gar!

Ilesa takes an interest in Tove while he's running through the main bits of the Agent class story, he's been on her radar for a while at this point because she's one of Darth Marr's enforcers and deals pretty heavily in inflicting tons of damage, eliminating targets, and being used as a threat -- she deals a lot in intelligence gathering and spy work as a means of making this easier on herself. She doesn't trust many people, and this helps her know the validity to the best of her ability of her info. Darth Jadus has... tried to persuade her to join him but the girl is loyal through and through to Darth Marr. So, naturally she's interested in some of Jadus's people, or at least in keeping tabs on them.

To get into how she sees Tove sort of mirroring what she went through in a way that reminds her of herself, there are a few things about her backstory that you should know. Like Tove, she is from the Chiss Ascendancy. She developed her force-sensitivity at a very young age and had the Third Sight. she was quickly given over to the state to train in order to become a sky-walker. But this is where I will say the account Ilesa knows differs from what actually happened. I'm still sorting out exactly what did happen and can say it was an unsanctioned experiment that a Chiss Admiral caused extreme harm to her in order to hide what he had authorized. The result is that Ilesa has a cybernetic implant with a jack that can be plugged into a nav console and she can interface directly with and fly a ship with her mind. At extreme risk to her, and doing so causes immense pain. She was forced to do this several times (she doesn't know how many).

She was ultimately found by some Imperial scavengers, floating in an escape pod, malnourished, freezing, and choking on the air which was largely carbon dioxide at that point. She was brought before the sith and gotten back into enough of a healthy state (she had fingers amputated and cybernetic ones installed due to frostbite) that she could stand on two legs, and taken to Korriban. Her first master was... Not great. He treated her like trash, manipulated her, made her work like hell, and tried to seduce her at the same time (it was a bad time all around for her), but Darth Marr killed him and saw something (a survival instinct and a desire to burn/electrocute things plus very clear and obvious gratitude that could be shaped into loyalty) in her that he could use. He took her in as his apprentice and the rest is history.

Ilesa sees someone that's also struggling to figure out who they are that is being pressed into a box at every turn. Someone that's angry. That wants revenge. That's been beaten down again and again, but is still hanging on. There's a ruthless efficiency to him. He's a survivor, even if he doesn't always know why he keeps trudging forward. And so is she. They've both fought to keep going. They've both been under someone's control that sucked. They've both been broken and put back together with cybernetic parts. They both need someone to protect them to some extent. Someone to hold a leash and say "they're under my protection" and to point them at a direction and say "go cause way more than a little chaos." Initially, there's some skepticism that the person holding the leash isn't going to beat them with it, but eventually that fades to loyalty.

Ilesa might still have a bit of the Third Sight in her, because I think she knew how much they kind of mirrored each other than we did. But she steps into Tove's story in person on Corellia to offer him both protection and a job, but on his terms (as much as they can be). She does this out of genuine curiosity, but she'd be lying if she said she didn't feel a tug, like there was something familiar in him. But the more they interact and the more he doesn't at all surprise her with his behaviors and reactions, the more she starts solidifying this thought that his soul mirrors hers. They don't have to do a lot of talking to sus one another out. A lot of their understanding of one another comes through watching actions. She proves pretty early on that he's her first choice. Why? Because he's interesting and he reminds her of herself. Because he deserves it in her mind. And maybe because she wants to be told or shown the same thing.