Hi there.
The central pin in the Magsafe connector in your charger and Mac is a data line used for communications between the charger and the logic board.
When you connect an original charger to your Mac, the LED on the connector goes green. A the same time the charger applies a lower voltage to the logic board (around 6V), which is enough to power the relevant charger controller circuit. If the SMC (a chip inside you Mac that supervises power related functions) find no issues from the several sensors inside your Mac, it talks back to the charger and gives the "OK" signal.
When the charger receives the "OK" signal, it raises the output voltage from 6V to around 19V and the battery charging begins (LED is now orange).
The non-original charger doesn't "talk" to the logic board. It just send the 19V immediately. Since your Mac has some issue with the communications between the charger and logic board, the original can't work since it never receives the "OK" signal, but the non-original can since it never waits for it.