That is rather odd. You can, however, do the following to get it to save the data for you.
Put the card back in the original device. Then connect that device to a computer via USB cord and copy or move the files from the card (and the device if there are any) over to an empty folder on the computer. Once done, then you can place the card in the new device, and once working in it, connect that new one to the computer via USB cord and copy or move the files over to the new device. I would suggest copy as this will leave them on the computer also, as a backup.
You can do the same but by uploading the files to a cloud account from the old device, and then download them from that account to the new device. You would need access to WiFi or Data through a carrier/service provider, to use this option.
Also, I have to ask, since the new one is asking about formatting, if by any chance the card is currently set as "Internal" storage rather than the standard "External" storage. I ask because then no other device would ever be able to read what was on the card when it isn't in the original device as it was encoded to that device when made "Internal". In this case, if you did it to put apps on the card, then that stuff won't be movable anywhere. The apps. Only other files can be moved, apps must be redownloaded if want them on a new device.