Tsuyu is not one of his shinki but a plum spirit who stayed with him for over a thousand years out of love even during his violent years. While his opinion is never directly stated, it is evident he cares for her and respects her opinion especially since he made her his guidepost despite the fact she is not a shinki because he knew that humans are capable of deception and betrayal, traits that a flower does not understand. She is usually the one who keeps him in line when he becomes angry or says inappropriate things.
Mayu respects Tenjin as her master and sees him as far superior to Yato. The two both get along well, with Tenjin proudly rubbing in Yato's face how she is a fine spirit who left him and the two both make fun of Yato's vagrant life and lack of popularity as a God.
He seems to get along with his shinki though it is implied he prefers females. However, should one of his shinki blight him even once he will have them undergo ablution and release them. This is considered a merciful act because the shinki could turn into ayakashi and even if they are released they can still find a new master. He does this to protect himself since not keeping check of being blighted will lead to the master suffering.
He tends to make fun of Yato and his lack of a shrine or followers. However, he does give Yato quite a few jobs. Yato in turn tends to be annoyed with Tenjin and after Yukine becomes a blessed regalia brags about this to Tenjin. Despite this, the two do have a serious relationship as Yato begged Tenjin to send him to the heavens so he could save Hiyori as he was not yet recognized as a God and didn't have a shrine which Tenjin did despite the trouble he could get into.
He seems to get along with Hiyori who in turn respects him as the God of Academics. He frequently warns her to cut off her ties to the Far shore because she is part of the Near Shore and it could be dangerous for her, showing he cares for safety. He also tells her to live her life since she is still young.
He seems to get along with Yukine, telling him when they first met that he shouldn't bow to another god as it was disrespectful to his master but said it politely since Yukine recently became a shinki. When Yukine wanted to be his shinki, he didn't seem to mind the idea but told Yukine he needed to first make sure that Yato release his name because he didn't want to turn him into a stray. He also believes Yukine is turning into a fine person despite Yato being his God; however, Tenjin seemed to be negatively critical on Yukine after Yato was stung so badly because of the boy's actions. He was surprised Yukine became a Blessed Regalia for Yato and lauded his progress.
Not much of their relationship is shown but they seem to get along since the two are currently collaborating to see who the sorcerer is.
He tends to get annoyed with her since her bad luck is contagious and can negatively affect him and his followers, as shown when after being hugged by her, one of his followers' sons failed to get into his choice college.