Well, in English, you can't say he has helped me yesterday. The present perfect tense doesn't work with temporal phrases that indicate finished times.
The -me- tense in Swahili is very similar to the present perfect in English but it, as far as I know, has no such restriction. It's main thing is that it indicates that the action's consequences are still current, so this probably means that what he helped me with yesterday is fine now and I don't need help with it now.
That's as far as I know anyway.
Is it really completely wrong to say "he has helped me yesterday"? I'm not talking about the grammar books now; I'm taking about whether a native speaker might ever use it. E.g. Emilian: has Rashidi helped you, as he said he would? Esther: yeah, he's helped me, already yesterday.
Does it sound completely wrong or..?