tsi- this prefix refers to a specific time referenced in the conversation, "yesterday". Maybe we can understand it as meaning, "at that time...".
wi- this prefix establishes the direction of the action as moving away from the speaker, leaving the listener with a sense of distance "away from" the speaker. Maybe we can understand this as "I worked over there...".
d- this prefix "de" is a plural prefix. When the following prefix begins with a vowel the "e" is dropped, thus: agi- becomes dagi-. A possible reasoning for using the plural prefix with the verb "to work" may be the idea of doing many tasks.
agi-- "I", this is a "B" Class bound pronoun, used before a consonant.
-lvwisdanel-- past tense verb stem for "work"
-v'i- past tense suffix. In conversation the "i" is usually dropped, thus "dagilvwisdanelv".