It is established early on in Naruto that one of the fundamentals for success in a shinobi mission is teamwork. This trend continued in Naruto: Shippuden, where the loyalty of a one's teammates could spell the difference between life or death. In turbulent times, teaming up was a necessary gamble. The only way to be completely sure one wasn't getting double-crossed was if they could somehow control their teammates -- and for Sasuke Uchiha, that's not entirely out of the realm of possibility.
Right after Sasuke defeated Orochimaru and absorbed his former master's essence, he set out on a journey to form an elite shinobi squad. Given his limited pool of options, he selected his team from Orochimaru's subordinates and experiments. First he recruited Suigetsu, a member of the Hozuki clan and master swordsman who could transform his body into liquid. Next was Karin, an Uzumaki with extraordinary healing powers, and finally Jugo, a kind-hearted soul who had the unique ability to unconsciously absorb natural energy.
Jugo's transformations had an unusual side effect. When he absorbed natural energy to a certain limit, he'd transform into a mindless beast hell-bent on destroying everything around him. To avoid hurting anyone around him, Jugo shut himself away and let Orochimaru perform all manner of experiments on him. His only condition for joining Hebi was that Sasuke prevents him from causing harm during his episodes. Given the power boost the nature energy gave Jugo, it was a tall order -- but Sasuke was up to the task.
Sasuke took care of Jugo's rampages by placing him under a genjutsu each time they happened. His Sharingan had improved a lot since he first awakened it during Naruto's "Land of Waves" Arc. During his fight with Deidara, Sasuke's feats caused even Obito Uchiha to marvel at what his eyes were capable of, declaring that they would soon surpass Itachi's. All it took for Sasuke to cast high-level genjutsus on Jugo was a simple glance, and he suffered no immediate drawbacks afterward.
After one such incident when Sasuke restrained Jugo, Suigetsu and Karin marveled at his power and have a short conversation about their reasons for following him. To their surprise, neither one can come up with a satisfactory reason for why they stayed at Sasuke's side even though they're both free to leave. Of course, Suigetsu did owe Sasuke a favor for freeing him from captivity and Karin did a terrible job of hiding her crush on the breathtaking Uchiha, but those alone don't seem convincing enough to explain why they were so attached to Sasuke. A theory that explains their loyalty, however, is that Sasuke had both of them under genjutsus as well.
Sasuke having all of Hebi under genjutsus would explain several aspects of the team's character and even its formation. He chose to recruit each of them personally, meaning he had the opportunity to place them under genjutsus during their first meeting. If he was fully convinced of their loyalty from the start, he could have summoned them to his side from their various strongholds. After all, for all intents and purposes, he was Orochimaru, their former master.
Hebi followed Sasuke into the most dangerous of situations with almost no regard for their own safety. Together they traveled the world, battled a perfect Jinchuriki and invaded the Five Kage Summit. For a group whose members didn't care about Sasuke just a few months before, it's hard to imagine they'd go to such lengths of their own free will. Even after Sasuke left Jugo and Suigetsu for dead and literally tried to murder Karin during his fight with Danzo, their loyalty didn't waver. None of them thought twice about returning to his side during the Fourth Great Ninja War and all Karin got was a very casual apology.
An undetectable genjutsu was quite within the realms of Sasuke's power in Naruto Shippuden, even before he formed Hebi. When he fought Orochimaru, he was mentally powerful enough to resist getting taken over by arguably the most powerful Sannin. Even Deidara -- who had specifically trained to withstand the effects of a Sharingan -- was helpless against him. By the time Deidara realized he was already under Sasuke's genjutsu, it was too late. Placing both Karin and Suigetsu under a genjutsu, neither of whom bore particular animosity toward Sasuke, would have been child’s play. It's also exactly the kind of thing the overly cautious and pragmatic Sasuke would do.