The claimed effect is implausibly large. The $1,000 in the title is cumulative over the first 14 years of life, not per year. Even if we assume that it's concentrated in the first five years of life, this implies that an extra $600 in income per year reduces criminal convictions in late adolescence by a third. If we assume that it's spread out over the whole 14 years, it would be a little over $200 per year.

Rather than measuring actual EITC benefits received by families, what they did was simulate the effects of variation in EITC policies between states and over time to estimate how much more or less a family would have received than the mean amount. This is highly vulnerable to confounding by, e.g., the secular decline in crime coinciding with increased funding for the EITC. This concern is limited but not eliminated by the fact that they grouped the children into 5-year birth cohorts. It is a bit suspicious that they didn't treat date of birth as a continuous variable. Furthermore, any number of other state-level factors could confound state-level differences in EITC policy.

Between the implausibly strong effect size and the methodological weaknesses, it's unlikely that they've identified a true causal effect here. There may be one, but probably not of the magnitude claimed here.