After Kai Xin's condition was stabilized, they transferred her to ICU for further observation. Dr. Phillip was afraid that she might have another attack, so he arranged to be on shift with the other doctor who operated on her.
Even though he had only slept for 4 hours last night, Dr. Phillip offered to take the first shift. After all, no other doctors would know DX's temper better than him. The next few hours, DX would be impatient and cold towards everyone, and Dr. Phillip did not want to come back in a few hours only to find resignation letters on his desk.
In addition, since he was the original doctor in charge of Kai Xin's condition, he should be the first person to stay.
As for Little Monkey, she was placed under the care of the best nurses in NICU. DX wanted her to be placed in ICU so that he could look after her as well, but due to her current condition, Dr. Phillip refused it.