Very true and what you said about cutting a perfect circle if the lathe is shaking and you aren't is absolutely spot on. The rubber feet in the link are for "leveling" a machine if the floor isn't exactly flat, but do not expect anything else from those rubber levelers. As Odie and several others have said, it is best for all fours to be making hard solid contact with the floor.
NOTE: You can also find pads that are called "vibration isolators", but their purpose is not to reduce the vibration of the offending machine, but instead it is to reduce the level of vibration or noise that is impacting people or other nearby machines that are mounted on the same surface (for example, floor or bench top).
Something that I always spend some time doing before I start turning is to balance the piece of wood between centers. It's not at all difficult ... it just takes some time. The goal is to balance the piece well enough that it doesn't have a heavy side that always rotates to the bottom. The spindle needs to be able to rotate freely so I will use either a point type center in the headstock or remove the drive belt. A live center in the headstock could also be used. It is really nice to see a large rough hunk of log spinning without a hint of vibration. Once in a blue moon, I will get a piece that defies balancing even after it is perfectly round. There's always a 3σ outlier to make life more interesting.
I think the vibration problem is often overstated. Try the lathe without doing anything to see what you think that you need to do, if anything. I suggest trying sand bags before bolting the lathe down. I am no expert on post tension slabs, but I suspect that the warning is there because you might drill into a post-tension cable and cause it to snap. You will be the first to know it if you do break one. You can probably check the exterior of the slab to find the locations of the post-tension anchors. You might even be able to find their locations by using a stud finder or a metal detector.