Extensive cross-linguistic work has documented that children up to the age of 9–10 make errors when performing a sentence-picture verification task that pairs spoken sentences with the universal quantifier every and pictures with entities in partial one-to-one correspondence. These errors stem from children’s difficulties in restricting the domain of a universal quantifier to the appropriate noun phrase and are referred in the literature as quantifier-spreading (q-spreading). We adapted the task to be performed in conjunction with eye-movement recordings using the Visual World Paradigm. Russian-speaking 5-to-6-year-old children (N = 31) listened to sentences like Kazhdyj alligator lezhit v vanne ‘Every alligator is lying in a bathtub’ and viewed pictures with three alligators, each in a bathtub, and two extra empty bathtubs. Non-spreader children (N = 12) were adult-like in their accuracy whereas q-spreading ones (N = 19) were only 43% correct in interpreting such sentences compared to the control sentences. Eye movements of q-spreading children revealed that more looks to the extra containers (two empty bathtubs) correlated with higher error rates reflecting the processing pattern of q-spreading. In contrast, more looks to the distractors in control sentences did not lead to errors in interpretation. We argue that q-spreading errors are caused by interference from the extra entities in the visual context, and our results support the processing difficulty account of acquisition of quantification. Interference results in cognitive overload as children have to integrate multiple sources of information, i.e., visual context with salient extra entities and the spoken sentence in which these entities are mentioned in real-time processing.