The new methodology for measuring poverty, while fair, is considerably impacted by residential expenses such as mortgages, rent, and utilities. Liberal states that have enacted greater minimums are also - generally - more densely populated and thus the poverty rate is skewed by factors in which minimum wage has no impact. Comparing the cost of rent in New York City or San Francisco to Atlanta and other Southern cities is obviously flawed.
When you factor out real estate, the states with the smallest poverty rate are New Hampshire, New Jersey, Vermont, Hawaii, and so on.