Presumably this question came up in the lesson on the narrative tense.
From the tips & notes:
The time infix -ka- is used to describe a series of past events. The sentence begins with the -li- tense on the first verb and then it is replaced with the -ka- infix in the next verbs in order to denote that the narrative is in past tense.
Too bad they didn't follow their own tips in this example, but maybe it's a context thing, e.g. the past tense prefix -
li- came up in the previous sentence. That's the way it works in the example they give in the notes (confirming the comments here by Theluji and BwanaSimba):
alipokwenda kwa dada yake kumtembelea, akampikia chakula. Baadaye wakala, wakazungumza, halafu wakaenda Mjini."
(This weekend, when Mkude went to visit her sister, she cooked her food. Later they ate, they talked, and then they went to town.)