It is permissible for a party to bring case in support of their position with them to a hearing. Although, the case law is not necessarily introduced as "evidence.". It would be a different story if they were trying to introduce some sort of substantive evidence at the hearing, which had not previously been provided to you i.e. a notice of acceleration, assignment, etc. Rule 1.130 of the Florida Rules of Civil Procedure covers what needs to be attached to the pleadings.
Sounds like it was used as calling legal precedent to the Judge's attention - not as evidence (i.e., facts) in your case. There is nothing improper with that which is why you should consult a local attorney. If the "shoe were on the other foot" - imagine if the highest court in your state ... or if the United States Supreme Court, for example, issued a ruling in a case that changed the way the law involving something important to your case should be interpreted. Then imagine if you heard about it and brought it up at a hearing that afternoon. It wouldn't change the facts of the case but the Judge should certainly apply the new law that favored you to those facts. Unfortunately there is much truth to the old saying about he (or she) who has himself/hereself as a lawyer being foolish ....
These are general thoughts - they not intended as legal advice - so you need and should contact an Attorney for actual advice on this situation.
I am not licensed in Florida but I know of no jurisdiction where a lawyer must give an opposing party advance notice of the legal argument the lawyer is going to make and the case law in support of that argument. What the lawyer in your case pulled out was a case with some legal principle in it the lawyer thought supported his argument. It was not "evidence". Usually if there is briefing before a motion the parties will cite the cases and the law they each believe they support their respective positions and then you can look at those cases and get prepared to tell the judge why they don't really apply or why the judge should not follow them. Must not have been any briefing in your situation. But there was nothing wrong with what the lawyer did.
I am not your lawyer and an answer on AVVO is not intended as legal advice but is provided for general informational purposes only. If you desire legal advice, please consult a lawyer and form an attorney client relationship.