The evidence that bilingual children develop stronger executive function is compelling but contested. Many studies suffer from confounding socioeconomic variables - bilingual households in Western study samples tend to be more educated and higher-income, which independently predicts cognitive outcomes. A longitudinal study properly controlling for SES, age of acquisition, and language distance would go a long way toward settling this.
Exactly the kind of specificity the review needs to address. This is useful context for the methodology section.
The SES confound is the main reason replication has been so difficult. The bilingual advantage studies that found executive function effects mostly came from communities where bilingualism correlated with higher educational attainment. Later studies in communities where bilingualism is the norm (Wales, South Africa, parts of India) found much smaller effects.