The way I understand it is that ammonia acts as a cleansing agent to cleanse away the present situation, while the turning over or reversing of the bottle and writing (reversing the writing and turning it upside down) represents turning the situation around to it's opposite.
Ammonia can also be used in floor washes and in cleansing baths - in greatly reduced quantity such as a teaspoon to a bathtub. This stuff is strong, and you have to be very careful when using undiluted ammonia.
Ammonia can be used as a substitute for urine because urine contains urea which is related to ammonia. But I have not heard of urine being used as a substitute in an ammonia jar - I guess you could in a pinch, but I'm not sure it would contain enough urea (ammonia) to turn the situation around. If one's urine has a strong ammonia odour, then there is a kidney and/or diet issue.
For an ongoing situation, even once turned around, keep the ammonia jar, for example a house that is always rented out to people who disrupt your peace. Otherwise, once the situation is turned around, some use the traditional hoodoo disposal methods of running water or crossroads. I don't do that, and instead pour the ammonia down the drain (we have a septic tank), and throw the paper into the trash, or let it dry and burn it. The bottle can be washed and reused.
There you go. Autumn Moon has it down. Thank you for the clarification and knowledge! Your explanation makes way more sense than what I was talking about.