I have the same problem
I had 330 photos (500MB) in directory xxx
I selected these files, cut them and pasted in directory yyy
both directories are on the external SD card (FAT32)
moving files on the same partition should take less then second but it took few minutes
then alert appered saying that AirDroid can't move files on external SD card
but despite that files were moved
then I downloaded directory to my pc and found out that airdroid duplicated some of the files (416 files instead of 330)
sometimes files were empty (0 bytes) and sometimes fully duplicated

I use Airdroid for more then 2 years but I haven't use cut/paste feature on more then 5-10 files before
Phone: ASUS Zenfone 5 (A501CG)
ROM: Stock
Android: 4.4.2
Rooted: Yes
Using wifi and Firefox on Linux Ubuntu
SD card: 8GB (with almost no files)
I had 330 photos (500MB) in directory xxx
I selected these files, cut them and pasted in directory yyy
both directories are on the external SD card (FAT32)
moving files on the same partition should take less then second but it took few minutes
then alert appered saying that AirDroid can't move files on external SD card
but despite that files were moved
then I downloaded directory to my pc and found out that airdroid duplicated some of the files (416 files instead of 330)
sometimes files were empty (0 bytes) and sometimes fully duplicated

I use Airdroid for more then 2 years but I haven't use cut/paste feature on more then 5-10 files before
Phone: ASUS Zenfone 5 (A501CG)
ROM: Stock
Android: 4.4.2
Rooted: Yes
Using wifi and Firefox on Linux Ubuntu
SD card: 8GB (with almost no files)