Admiral Vance is testing the character of the crew. He told Saru to offer Tilly the position to see how the rest of the crew would react. Stamets reacted normally, in a very upset manner initially.
However, Vance's dismissive attitude towards Adira Tal is hurting him now. Adira told Stamets that she remembers from Admiral Tal's memories that Vance often uses this ploy to test the character of the crew. Note Stamets' sudden change of attitude and quickly letting the rest of the crew in on the plot, showcasing their "supportive" manner and foiling Vance's plan to try to get the crew to act like jerks.
However, Vance's dismissive attitude towards Adira Tal is hurting him now. Adira told Stamets that she remembers from Admiral Tal's memories that Vance often uses this ploy to test the character of the crew. Note Stamets' sudden change of attitude and quickly letting the rest of the crew in on the plot, showcasing their "supportive" manner and foiling Vance's plan to try to get the crew to act like jerks.