Translation:To arrive on time
Yes, -wahi has these meanings of: be on time, be prompt; reach, arrive (on time, at the right time). Interestingly though, -wahi also has the meaning of 'have ever' with POSITIVE tenses, and 'have never' in NEGATIVE tenses: aliwahi kumpenda mtu ijapokuwa siku moja katika miaka tisini aliyoishi = did he ever love a person even for a single day in the ninety years he lived; sijawahi kumwona rais = I have never seen the president.
Kind of, technically speaking words only have the meaning that is given to them by speakers of the language. Words are more tied to thoughts than they are to words in foreign languages. I have heard native speakers describe this word, and use it in a manner that directly relates to specific instances of arrival. So it's not entirely wrong to say that it means "to arrive on time," even if that isn't always the best translation.
I can see how it can be used with an implication of arrival. Arrivals can be be on time or late, I get that. However, it could also be used with other activities that can be on time or late and at a beginner level in a beginner course, I think it would make more sense to translate it as a general sense of being prompt so that it won't be assumed that arriving is the only context in which it is appropriately used. I know from personal experience that this sort of thing can be hard to unlearn when tied too closely to a particular use, especially when learned at an early stage.