When this kind of compatibility is required, they mostly mean mechanically, vibrations and things like that. The software isn't written, nor the conops, and other tests haven't likely been done. In theory, however, this allows one to, in the event of a major issue, launch on another rocket, with some work. I strongly suspect Crew Dragon is rated for at least Atlas, for instance.
I'm quite sure it will never be flown from a Delta IV. There are no new missions planned for that rocket, soon Vulcan will completely take over there.
Vulcan is another question entirely. I'm quite sure that once it is available, ULA would like to launch using the Vulcan. This will take some time, but I expect that in 10 years or less, Vulcan will become the primary launch vehicle for Starliner.
As to Falcon 9, SpaceX would actually have to allow it to be used, if requested, for a number of reasons. I'm sure at least a basic level test has been done, but most likely this is not complete. Cygnus at least for a time considered flying on Falcon 9 when the Antares rocket blew up. The only reason why this would actually be done, however, is if the Atlas rocket had a serious issue. I can't imagine this to be the case, but it is good to at least make sure that the payload is comparable with the rocket in the event of a major emergency.