It sure sounds like your system is failing. Water inside the riser (or on top of the tank) is proof that they system isn't working correctly and is backing up.
This is a nuisance and a health issue. Be sure to notify your landlord that the system appears to be failing. He/she should then contact the local Health Department and follow their procedures to get it repaired.
Just covering this won't fix the problem.
If your landlord ignores the problem, you could call and complain to the Health Department. This approach will likely cause relationship problems between you and your landlord and possibly make your life very stressful.
The friendly approach is always better.
