The feat, since you did not post the text, and it pretty readily answers your question:
Benefits: When charging an opponent while mounted and wielding a lance, resolve the attack as normal. If it hits, you may immediately make a free bull rush attempt in addition to the normal damage. If successful, the target is knocked off his horse and lands prone in a space adjacent to his mount that is directly away from you.
Emphasis is mine. I can't see how someone would land "in a space adjacent to his mount" if no mount is at all in the equation.
By RAW, if the target isn't mounted in a horse, you can't unseat him? :P
No, the feat says what happens if you are successful in the attempt: the target is knocked off his horse and lands prone in a space adjacent to his mount.
Seriously, I think you are trying way too hard to make something that is very simple and clear into something it's not. If you want a feat that does what you're suggesting, talk to your GM and ask for that feat to be created for you -- but don't confuse a bunch of people who may run across this thread.
There are a lot of feats where the wording is really sketchy or ambiguous, and it leads to some really good questions.
This isn't one of them.
The intent is clear which is to knock someone off of a mount. The rules are not written in legalese so one must use the wording to figure things out.
Quite honestly, if you want to go argue silly RAW interpretations, this could literally teleport someone halfway across the world to a horse owned by them, and they'd land in a square adjacent to it, directly away from you.
See how dumb that sounds?