I also live in the Miami area and have had several AC units replaced in the past few years at my properties. First thing I will tell you when it comes to HVAC, especially in our climate is that never take the lowest bid from any contractor down here. $250 for all the work you described is EXTREMELY low and I personally would never hire anybody who quoted me that. If you provided the units and just needed installation then I would expect easily more than 1k for somebody competent to do the job.
That being said, regardless of how low the quote was, you paid for a job and clearly the unit isnt working. I would not pay them the full amount until they send somebody out to fix it, and you need to ask for an invioce which shows exectly what you are being charged for. I doubt at this point they will put a lien on your property. Good luck!
