I just did this in my basement and talked with the Co that installed it on how to do this. All that I did was get a 2x6 and measure the width of your track that your tile lays in. Cut the wood that that lenght, best to do the short side of the track if you have a2x4 tiles.
Now, where you want the fan, keep that tile in place and lay the 2x6 on TOP of the tile from up above. Then run screws in from the side through the track and then into you 2x6 on each side to secure it. I just used drywall screws, worked pretty good.
Now, from down below, just drill your hole for your wires to run though and just use the mount that comes with fan, since you will be running the screws into the 2x6 you just put up there.
I have had mine like this for about 6 month and the fan has never shut off and has worked great. The tracks for a drop ceiling are stronger than what most people think. This what the Install Co. does when people want fans in their basement.
I hope you understand, since I sometime do not describe thing very well
