I haven't tried what exact steps are involved, but can tell you that the initial release of the Komplete Kontrol software did not allow to output MIDI from the Arpeggiator into Logic (or other DAWs). This feature was added in the latest Komplete Kontrol update, though.
So, first thing to make sure of, is to go into NI's Service Center, and check if an update is available for Komplete Kontrol. If so, install it, to be at least a step closer to what you're looking for 🙂
If you're still stuck with this, I should be able to try this in the coming days and post what steps are needed.
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