As you likely know, stones like cubic zirconia (CZ) need to be clean to look the best. When clean, a nice CZ will sparkle and look great. However, when just a little dirt soils the back of the stone the shine quickly disappears. That is the nature of the stone. It simply does not have the ability to return light when dirty on the back(bottom of stone, called the pavilion) in the way a diamond does.
For cleaning most gemstones, glass cleaner should work just fine. Some people use toothpaste, of all things! I do not recommend that since toothpaste can be abrasive and can dull the metal.Glass cleaner is a generally good choice with one exception.
The Exception. Sterling Silver will react badly to ammonia. If the glass cleaner contains ammonia, do not use it on sterling. You may not notice any problems and this might be because the sterling has a protective plating of another metal on top of the sterling. The plate is very thin but durable and is there to prevent the ususal natural tarnish of silver.
Ammonia will speed up tarnish and can leave whitish spots on sterling. I would avoid getting the cleaner on sterling. If you need to, you may clean a stone set into sterling with a mild detergent such as "Joy" which is a dishwashing detergent. Never use soap since a soap film might be left behind.
The ingredients in glass cleaner are very much like those in some over-the-counter jewelry cleaners. By your discovery, you have found an effective method to clean the stones and save money at the same time. That is a good move. Keep in mind, no cleaners including glass cleaner should be used on stones which might absorb the cleaner or be affected by it. These are pearls and turquoise, for the most part. Wash these stone is a mild dish detergent and rinse well then dry gently with a soft cloth.
Topaz is perfectly safe for almost all cleaners except abrasive ones. Ammonia is fine for topaz and CZ and does a good job. As I said, do not use ammonia with sterling if that is the metal your gemstones are set into. In any case, rinse well with lukewarm water to remove all traces of cleaner and pat dry. That should do it. You may use a soft brush to get behind the gemstones.
I am very happy to see a person who is interested in caring for their jewelry. We see so many rings and other jewelry items where I work which are terribly dirty. Often, the settings are worn and the jewelry is too dirty for the owner to notice the danger of loose stones. People will say, "I never take off my jewelry".
That is the biggest mistake they can make. Regular cleaning not only makes your jewelry look the best but also gives you a chance to check for wear on the settings and gently touch the stones to see if secure or loose. Caught in time, a stone may be easily and inexpensively tightened in the setting.
Let it go and the setting may have to be remade at much more cost. Good to know there are folks out there who do care enough to clean their jewelry regularly. Often times there are people that come in to have there jewelry cleaned, then we are the ones that have to tell them that there is a stone missing or that they are going to need a whole new setting for there stones because they never took care of there jewelry. Which in turn will cost them more too have to have there stones taken out and then put into another siting.