How does the TP4056 overdischarge protection work?
Am I seeing it wrong?

Yes you are. Indeed the OUT+ and B+ connections are shorted but are the B- and OUT- also shorted? No, when the MOSFETs in the FS8205A are off, the battery - connection is disconnected from OUT-
The TP4056 isn't doing the protection, the DW01A is taking care of that.