Musk had many reasons for not chasing after Rong Shi, other than the fact that she had some life-saving means. She would not stay in place and wait for him to attack, from the moment she learned it was almost impossible to win against him she would keep running until she found a safe place to hide.
Musk on the other hand had a feeling that the oppresion from the tribulation was increasing his time on the run. He had to recover, at the same time understand the changes that had occurred with the breakthrough of his physique.
More than that, he was going to take advantage of the remaining time to make sure that the longevity art, breakthroughs. But he was not sure if he could be done by the time he had to face the tribulation, still, it was not a bad move to attempt as immense unique power could be added to his body if he succeed.