Use of the "safely remove" button is determined by your distribution who configure the underlying Linux systems. In order to speed up file operations, the Linux kernel uses a cache where your files are copied to. On some distributions, this behaviour is disabled for USB storage devices.

If the cache is disabled then the files are copied immediately at the time on to the device. When you "safely remove" the device, the device is unmounted and the kernel flushes the cache to disk.