Nope. If your secure in your yourself and your relationship being jealous in this situation is very dramatic to me.
Now if they were grown men and Jinsung was relishing in it I could see being jealous but other wise it’s harmless compliments your partner is getting. Enjoy the fact that you get to be with someone hot lol.
Really if you think about it to be jealous is basically saying he thinks jinsung is easy. Easily swayed which he by all evidence is not.
Based on yura's character, its not that he thinks jinsung is easy or will fall for someone etc. its just that yura is obsessed with jinsung, obviously, so regardless of the premise whether jinsung is getting hit on or the other way around, if a leech comes close to his jinsung, he loses it, he gets jealous. Based on the whole story itself, we can see how unstable he is. Also take note that his characters merged w/o taking therapy so some of his deep hidden desires and obsession are still unstable and on edge--- like that jealousy part.

What’s is there to be jealous of lol?
1. They are children so pose no threat unless you think jinsung is a pedo.
2. Jinsung is super-duper gay and thems are high school GIRLS.
So this is a non-issue