Clinical reports suggest that children with autism spectrum disorder (ASD) struggle with time perception, but few studies have investigated this. This is the first study to examine these children’s understanding of before and after. These temporal conjunctions have been argued to require additional cognitive effort when conjoining two events in a clause order that is incongruent with their order in time. Given the suggested time perception impairment and well-established cognitive deficits of children with ASD, we expected them to have difficulties interpreting temporal conjunctions, especially in an incongruent order. To investigate this, the interpretation of before and after in congruent and incongruent orders was examined in 48 children with ASD and 43 typically developing (TD) children (age 6–12). Additional tasks were administered to measure Theory of Mind (ToM), working memory (WM), cognitive inhibition, cognitive flexibility, IQ, and verbal ability. We found that children with ASD were less accurate in their interpretation of temporal conjunctions than their TD peers. Contrary to our expectations, they did not have particular difficulties in an incongruent order. Furthermore, older children showed better overall performance than younger children. The difference between children with ASD and TD children was explained by WM, ToM, IQ, and verbal ability, but not by cognitive inhibition and flexibility. These cognitive functions are more likely to be impaired in children with ASD than in TD children, which could account for their poorer performance. Thus, the cognitive factors found to affect the interpretation of temporal language in children with ASD are likely to apply in typical development as well. Sufficient WM capacity and verbal ability may help children to process complex sentences conjoined by a temporal conjunction. Additionally, ToM understanding was found to be related to children’s interpretation of temporal conjunctions in an incongruent order, indicating that perspective taking is required when events are presented out of order. We conclude from this that perspective-taking abilities are needed for the interpretation of temporal conjunctions, either to shift one’s own perspective as a hearer to another point in time, or to shift to the perspective of the speaker to consider the speaker’s linguistic choices.