In the circle you drew, where the two ends are, the lower one has a 'point', just below that point is a crack in the 'rubber'? follow that down to where the crack leads to what appears could be a continuance into the post itself, and if so it would appear to curve down on the post... Again, 'appear' - from a photo this is only supposition. 1st hand inspection would be needed.
There are also 'chips', seen as small white marks which seem to follow that crack line, as you look further... Again, 'appear'...
The insert you call 'rubber' is clearly more brittle than a rubber compound. It may have elastomer properties, but fracturing as seen is not common to most elastomers, unless there's been some change to the material. The rib forms an I-beam type structure with the post, to limit flex.
That rib is there to support the carbon fiber arch of the post, and limit the 'flex - otherwise there's be a good possibility the post would assplode if put under a sudden, hard load.
My deduction is that the 'rib' assploded under a load (or multiple loads), with the possibility of some further damage starting on the actual Carbon Fiber.
Would it be presumptuous to ask how much you weigh?
Did you get the post or the bike New or Used? Is there a possibility that the seatpost already had some damage and you hadn't noted it prior to the rib collapsing? All worth asking/considering.
I'm not familiar with this post, so conjecture of what appears. But I'd be looking deeper if I was putting my butt on top that.
Ride On
Yuri