This paper argues that the semantics of the English epistemic modal should and Japanese indirect evidential yooda involves temporal requirements on the relation between the temporal denotation of their prejacent and the time in which the speaker acquires the evidence for the utterance (EAT, following the terminology in Lee (2013) and Smirnova (2013)). The English should requires EAT to come earlier than the initial moment of the prejacent's temporal denotation, while the Japanese yooda encodes the opposite temporal relation between these two components. I further propose that the differences between the two with regard to these temporal components can be parameterized with a micro parameter. The findings of this paper have two implications. The first is that there are evidentials that encode temporality but are not involved in the temporal inflection on the prejacent’s verb. The other implication is that the temporal relation between EAT and the prejacent's temporal denotation may be a universal semantic building block (von Fintel and Matthewson 2008).