Plumbing is weird. Last year we had a blockage in the main sewer line in the basement, thankfully I was able to snake it out- just barely avoided knocking over a somewhat (at the time) rickety set of shelves filled w/ paint cans w/ parts drawers full of screws & nails on top...
The symptom was air bubbling up thru the traps in the downstairs bathroom whenever the upstairs was flushed. No long hair here.. 1st time in 15yrs here that it happened. My brother rented a place a few years ago where they had a sewer line backup so bad they had to get a pro in to scope the pipe, he found a feminine hygene product a guest of theirs had flushed wedged into the pipe right were it joined the street sewer line.
If the people below you did not have a problem then the problem was above their lines into the plumbing stack but there's no guarantee you caused it- your pipes enter the main up/down pipe the same as everyone elses- anyone above you could have flushed something which somehow jammed things up.