I have a 1/2 bath on my first level and my basement is unfinished. Whenever the toilet in the 1/2 bath is flushed, the water leaks into the basement. From the basement, I can see the black sewage pipe that directly comes out of the toilet above, and when the toilet is flushed, water just comes from the sides of the black pipe on to my HVAC system! See attached picture #1 of the leaking black pipe as seen from the basement. The wood around it is all wet. Attached picture #2 is of the toilet and the tiled floor.

Note that there is no leakage/spill on the tiled floor of the 1/2 bath when the toilet is flushed. Also, the water gushes through into the basement only when the toilet is flushed; not otherwise.

Can you tell me what's wrong? Is this a job for a handy man or a plumber... reason I ask is that I have this standard coverage from Old Republic Home Warranty so I might be covered if I go with a plumber.

Leaking black pipe and wet wood as seen from the basement:

Toilet and the tiled floor: