Welcome to hobby-machinist!
You can tram the vise or tram the table, or both. It sounds like you were taking the vise off to tram the head to the table. You can use the ring on the vise, but now you are tramming the vise base, and not the table or the vise jaws. It depends on what you are trying to accomplish. There are possible addtitional errors whenever you use something on one part as a surrogate to measure something else. Whether that is enough to matter is up to you, but be aware of it. For a first time check I would tram the table side to side, and front to back, then tram the vise ring, and then tram the vise jaws and bed, looking for inconsistencies. Anything you find that is odd or off should require further investigation. A milling machine is a whole lot of parts all working together to produce results. They all need to be correct for the machine to be correct. Ideally...
Make sure all the axes of the machine are locked down when you tram it!