That adjunct job gave him sanity to solve the problem. In the case of Grigori Perelman, these universities (Princeton, Harvard) did not want to give tenure job after his proving Soul Conjecture; this was during his postdoc at Courant NYU.
Of course, these math guys wanna offer a tenure track position, which woulda prevented him from proving Poincare conjecture. He went back to Russia, spent time in isolation for 8 years or so. Proved it. Once he published the paper on arXiv, the shithead professors at Princeton, Columbia want him back, so that they can be co-authors of his paper on poincare conjecture or these universities can appear on the paper a la affliation: you see, these elite universities love to show "Mr X from Princeton solved poincare conjecture".
Another chinese professor at Harvard tried to steal the credit from Perelman for the same conjecture.
It is a big mess out there. Zhang somehow used his adjunct/tutor job to spend time in number theory. Perelman used his postdoc fellowship savings to solve his problem. IN Zhang's case, he got the tenureship after his proof; Perelman gave up math.