It's an astute question. I'll try to provide a succinct response, but Latin syntax defies simple descriptions for those interested in going deeper. Adverbs can appear in variety of locations and it can sometimes be difficult to determine a precise valency free of ambiguity, while other times context allows a precision. There is a discussion of adverbs of manner in Devine and Stephens, Latin Word Order. Structured Meaning and Information (Oxford, 2006) 101ff, who have a section on saepe (pp. 250ff). They argue (252) that clause initial saepe, as we have here in this DL sentence, has the sense "It is often the case that,""it often happens that." The DL sentence is short and devoid of context and the purpose at this stage has to be to assist with vocabulary and help students get a feel for the language. See the examples Devine and Stephens provide of saepe after a scrambled phrase on p. 254.