The mechanisms underlying the processing of the temporal reference of a sentence are still unexplored. Most of the previous psycholinguistic studies used the temporal concord violation between deictic time adverbs and tense marking on the verb to investigate this issue. They found that processing past tense marking is more difficult than non-past tense, indicated by lower accuracy rates and/or longer reaction time. However, it is not clear whether this complexity is due to tense marking or the temporal reference it denotes. This paper examines this issue with a judgment acceptability experiment in Taiwan Mandarin, which is analyzed as a tenseless language. The two modal auxiliary verbs you and hui were placed after deictic past time adverbs (grammatical with you but not with hui) and deictic future time adverbs (grammatical with hui but not with you). The temporal concord violation of the auxiliary verb you led to higher acceptability rates but longer reaction time than hui, reflecting higher processing difficulties. This paper argues that these complexities are due to the existential-assertive meaning of you, which interplays with the meaning of the event described by the verb rendering the situation more or less likely to occur in the future. The computation of the temporal concord of hui, displaying a future sense meaning, is more straightforward and therefore easier to process. This suggests that the mechanisms responsible for temporal reference processing are of different nature depending on the semantics of the temporal marker in the sentence.