Eye-tracking research has revealed that people rely more on a recently enacted action-event than consider a plausible future action-event when hearing a sentence referring to a visual scene. When participants encountered a recently enacted action-event, and then listened to a (NP1-Verb-Adv-NP2) past or futuric present tense sentence in German, they inspected the target of the recently seen event more often than that of the equally plausible future target shown, irrespective of sentence tense. These preferential looks towards the recent target persisted even when future events and futuric present sentences were presented with greater frequency within the experiment. The current experiments assessed whether the preferential looks toward recent targets occur in similarly structured English sentences containing earlier, more localized tense markers (auxiliary verbs: will/has), and in Georgian sentences containing an even earlier case marking at the first noun phrase (nominative and ergative case). Can the early morphosyntactic cues eliminate the preferential inspection of the recent target? Results revealed that when participants processed the tense marker in Experiment 1 (English) and 2 (Georgian), the bias towards looking at the recent target was reduced. However, in Georgian, the morphological marker on its own was not able to eliminate the strength of the recent event. In both experiments, participants rapidly started to decrease their looks towards the recent target when exposed to the clear future tense cues at the verbs and this gaze pattern continued into the later word regions. This shows that participants were able to use the tense cues but only partly use the morphosyntactic cues to anticipate sentence referents to the visual context.