Overhaul is the leader of his organization. He does not appear to have a level of respect or care for his subordinates beyond their use. This was evident when he used one of his subordinates as a human shield and chastises another subordinate for being slow.
Despite how he treats them, the members, particularly those of the Eight Expendables, value Overhaul as their leader and are willing to protect him. However, a few others respect his power but not necessarily his leadership and tactics.
Kai was taken in and raised by the Boss-man of the Yakuza. Kai views him as a father figure and believes he owes the old man a great debt for taking him in. Throughout his life, the Boss recognized that Kai was troubled and he would try to hone him into an honorable Yakuza. Kai would often lash out at anyone who badmouthed the Yakuza as a child. The Boss told a young Kai that Yakuza can't hurt innocent people but still thanked Kai for trying to protect their honor. This became a treasured memory for Kai as a reminder of his debt to the Boss.
But Boss's ideals and his own would often clash as Kai grew older. The Boss wanted Kai to stay away from villainy and drugs. He even refused Kai's plan to reinstate the Yakuza. Disappointed, Kai forced the old man into a coma. Even so, Kai still appreciates everything the old man did for him and only put him into a comatose so he could repay his debt.
After becoming Overhaul, Kai takes care of the old man and even talks to him at his bedside. The Boss man is the only person Kai appears to care for and that he's ever showed empathy for.
Chronostasis is the aide to the Shie Hassaikai and one of the few members Overhaul does not treat like a disposable object. This is most likely because Chronostasis's abilities are of higher use than most of the members which places him as a valuable asset to the organization. Also it’s been revealed that Chronostasis and Kai knew each other since childhood.
Mimic is a member of the Shie Hassaikai. Similar to Chronostasis, Mimic is treated as a valued member of Overhaul's organization and not considered expendable. Mimic is incredibly loyal to Overhaul. Despite being the Director of the organization, Mimic accompanies Overhaul during his exploits and protects him from potential threats.
Overhaul does not show interest in joining the League of Villains, due to their apparent lack of planning. He only sees their influence as a means for his motives. The League initially had interest in Overhaul and his organization before coming into a disagreement when Overhaul brought up his motives. The meeting causes a skirmish, resulting in casualties on both sides. Himiko Toga and Twice become immensely upset at the death of Magne and Mr. Compress's lost arm. Despite this unstable relationship on both sides, Overhaul still encourages the League to figure things out before contacting him again.
Overhaul treats Tomura Shigaraki pragmatically, as he wants to bring out the full potential of the League by having them work under him. After his meeting with Tomura and agreeing to work as equals, he employs Himiko and Twice into his services as he sees their Quirks as powerful but also to have the two under his control. However, Twice and Toga do not favor him and eventually sabotage his getaway plans during the Shie Hassaikai Raid.
When he is defeated by Izuku Midoriya and being transported to a hospital the League attacks the vehicle escorting him. Overhaul is not fazed by their appearance but he becomes angry when they steal his Quirk-Destroying Drug. His rage turns to fear as Mr. Compress and Tomura compress and decay off his arms as revenge for his actions against the League. Tomura taunts the helpless and powerless Overhaul for his "high and mighty" attitude and relying on his Quirk so much despite wanting to get rid of Quirks before leaving.
Eri is an important person to Overhaul. Similar to Chronostasis, Overhaul treats her better than most of his other subordinates because of her use.
From the information gathered by Sir Nighteye's office, Overhaul uses Eri's blood to create and sell his Quirk-Destroying bullets. In conducting his research to create the drug, Overhaul has used his Quirk to destroy and reassemble Eri numerous time proving he truly does not care about Eri as a person despite that she is the granddaughter of his beloved Boss. In return, Eri fears Overhaul and has been mentally scared by his tactics to get her to obey.