Tater/rai became human only after yeo ul loved him back, (they were already kind of dating, but yeoul wasn’t fully in love yet), so maybe when the uncle and the girl were together, they weren’t in love yet, that’s why she didn’t become human. Also, i’m pretty sure that she was never his gf, in the story they don’t talk about her being with him romantically, but surely the uncle was affectionate.
Hope i made it clear
As i said maybe:
1) they were only friends (i don’t see anything wrong with taking a photo like that with a friend)
2) they were dating but weren’t in love yet (there’s a lot of difference between liking someone and loving someone)
3) it was a one side love
Yeah, it could also be a hole in the plot, but if u think about it like that, then even star and tater should have become human right after.
In my opinion, Tater didn’t become fully human simply because Yeo-ul reciprocated his feelings, since that had already happened long before. Rather, it seems to have happened because they both confessed their love to each other for the first time that night. I also think Uncle’s affection for the girl shown was genuine and serious. My guess is that they simply never got the chance to confess their feelings to each other before the cat’s unfortunate death. And I don’t think Uncle was being a jealous hater at all, he was trying to protect his nephew from going through the same traumatic experience he had.

Did the uncle not love his girlfriend? Or did the girlfriend not love uncle enough? Why did she not turn into a full human?
Clearly he loved her so much he wanted to stop his nephew from falling in love with the tater to "potentially " have the same so called exposure
Personally, uncle is just a jealous hater