multi attack penalty wrote:You take this penalty on all attacks after the first on your turn.
Seems pretty clear, why should Cleave be an exception? It doesn't mention being an exception anywhere. It makes an additional strike attack on your turn => it adds to your MAP.
The addition in Twin Takedown and Flurry of Blows is likely in there to clarify that despite it being two attacks in a single action, you still need to increase the MAP after the first strike. Because it's a single-action "double-attack", people might otherwise mistakenly assume that the same MAP applied to both attacks.
With cleave, that wasn't neccessary to specifiy, because cleave is only one attack in the one (re-)action.
This is all interpretation, not RAW. The Feat description should tell you how the Feat works in regards of MAP, like Twin Takedown or Flurry of Blows. This leads to people giving their own interpretation on rules when worded poorly especially because Cleave is a single attack, it's just the same attack that kills the first creature then hits another one, you utilize another Strike roll to check if you hit it but it's not another attack.
It might be clear for you, but for most of others it's not, there is a discussion like this on Reddit and one on the Facebook group as well, which means it's not clear at all. I honestly don't know why the Errata did not address this.