There's a wide variety of hardware eject buttons for optical drives. Some of them send a software signal, so that the operating system knows that the disk has been ejected. Some of them do not do this. It sounds like your new system has an optical drive that falls into the latter category. Since optical drives tend to be slow, read-only media, there's a high chance that the operating system will have cached some of the data if you were using it. Removing the underlying storage without clearing the cache may not immediately result in the data being unavailable (although there is a strong chance that only some files, or even some parts of files remain available without the media).
The simple workaround is to always tell the software to eject, rather than using the hardware button. You might also look at alternate input devices that have an eject button (some keyboards, or wire a special button as an input device, etc.). The last resort would be to switch your optical drive for another one.
In the event that you have removed a disk without unmounting, it should be safe to unmount it from software independent of the removal of the media. Some drives will automatically rescan when this is done: others will physically eject and need to be reinserted.
