They don't consider each other family nor they are close, but Vesska doesn't mind. Living a cushy childhood full of great occasions was more than an orphan could ever ask for, and they always had one or more of his guardian's assistants to take care of all their needs. From their "uncle" they learned how to deal in politics, "become useful so they become needed", and use their words and charisma to always get their way, all skills they made a great use of as Commander. Other than ending up a bit emotionally constipated due to lacking genuine lasting affection during their formative years, there was nothing to complain about.

As for Phlunt's side of things, he wasn't all that interested to begin with. The decision was only made when the new Dean of Synergetics started vying for a seat on the Arcane Council and he was advised to make some grand acts of kindness to gain public favor, which included taking an orphan under his wing (picked without much care). They spent time together pretty much only during public events or the occasional private lesson to check on their progress, and the moment little Vesska showed interest in Lion's Arch he shipped them off to the best mentorship he could find. To his credit, Phlunt was never mean, just strict and open about not being interested in rearing young progeny, and Vesska quickly learned how to get anything from him by being his perfect little diamond of a ward to show off to others. By the time Vesska was a teen, they had come back from Lion's Arch and effortlessly got into Synergetics, and since their exam score was almost impeccable, people insinuated a lot behind their back. However, their troublemaker tendencies eventually confirmed that the only nepotism at play was the slap on the wrist they got for any mess they made. They were objectively brilliant, and the Snaff's Savant title was practically a given when they decided to join the contest. Phlunt was insufferably beaming with pride and maybe a twinkle of genuine affection for weeks afterwards.

All of this led to Vesska's and Taimi's relationship being juuust a little rocky at first instead of the canon bonding that happens during s2. In s1 Vesska felt kinship for a fellow orphan, but Taimi always kept a bit distant without ever saying why. Eventually the matter came up in s2. They knew their "uncle" was hard to deal with (the things they heard in College about him were even said to their face) and that did explain why she was always a tad more snarky and bitter towards the Commander, but they still took her comments personally at times (they did feel like direct jabs at times tfb). Still, they tried to mediate between Taimi and Phlunt when he showed up, successfully turning the situation to their advantage, but it infuriated her further and, when they asked why, she blew up at them for how easy they had it. Vesska managed to defuse the situation (with Braham mediating), but that started them down a path of unwrapping their upbringing and the way it shaped their relationship with others, overall making them a little less insufferable.