Clicking a button that only does a Perform Find with no stored find criteria will do what you are seeing - display a message that no records were found. This is because you did not enter in any valid find criteria and therefore no records were returned. Ideally you'd want to modify your button to run a script to do something like...
Enter Find Mode [Pause]
Entering Find mode and pausing will allow you to enter in your find criteria first before the find is actually performed.
As for the behavior of the button redoing your last find - I am somewhat surprised at that behavior but I was able to reproduce it. I'll follow up on my end to see if this is an actual bug or expected behavior (that it remembers what your last find was.)
Steve - this is the expected behavior that I have always seen. If you manually do a find, and hit cancel instead of Modify Find, it goes back to the found set from before the attempted find.
Perform find is the "action" telling FileMaker to perform the find. First enter Find Mode (this is what command-F does). Second step is Perform Find.
You can embed the find criteria in the Perform Find request by using the "Restore / Specify Find Request" option.