mv returns as soon as the files have been moved from the applications' point of view. If any program tries to read the files after
mv returns, it will find them on the USB stick and not on the hard disk. However, it is possible that the content of the files and the updated directory on the USB stick are still in the disk buffers and not yet written out to the USB stick.
If you pull out the USB stick without unmounting it first, there is no guarantee that the USB stick has all the data that it's supposed to have, or indeed that it's in a consistent state (it's unlikely, but possible, that old files will be temporarily unreachable).
Always unmount removable drives before disconnecting them.
sync mount option reduces the window of risk at the expense of making writes slower, but it does not remove the risk. It also kills older USB sticks faster.
The files may or may not still be on your computer. Linux does not make recovering deleted files easy. If this was a lot of small files, forget it. If this was a few big files, especially if the files have a recognizable format (pictures, mp3s, videos, …), you have a chance. Stop writing to the drive immediately: anything you write reduces the chance of recovery. If this is your system drive, download and reboot to a special-purpose distribution. If not, install carving tools with your distribution's package manager. See How to recover data from a bad SD card? for some tool names.