Will Solace probably learned to put aside his own needs and wants to help other people during tlo. After Michael Yew died, Percy tore Will away to save Annabeth. He didn't get to help look for Michael or even grieve for him; he had to save Annabeth. While he's healing her, Will says that they're lucky they got there when they did or else Annabeth would've died, which probably solidified that sentiment for him.
The same thing happens in tho and Will again puts his own needs aside to help save other people. At this point, his only siblings, Austin and Kayla disappeared, yet Will knew it was his duty to stay back and heal the injured. He even stopped Apollo from trying to find them at that moment.
Will probably had more concern for Austin and Kayla than Apollo at that moment. He already lost Lee, Michael, and the rest of his unnamed sibling during botl and tlo; he doesn't want to lose his remaining ones. Even though he experienced so much loss and thought he was going to experience more, he still stayed behind to treat the rest of camp because he had to.