They have most likely knocked a component off of the board responsible for the sensing circuitry, or forgotten to plug a part in. I do not work on many Mac Minis, but on MacBooks, the fan will spin high speed in these cases. The high fan speed isn't a fault with the fan or fan connector.
Whatever the problem is, it is not your responsibility to fix it. Take it back to whoever repaired it to either fix this or refund you, since they haven't done a proper job. It is irresponsible of them to tell you to try and alter the fan speed using software, they most likely knew it wasn't fixed properly and just wanted to get the Mac out of there.