What equipment did they use to get this data from your fob? If they used a proxmark3, it should be able to determine the tag type. If it is EM, HID ProxCardII, or Indala then the xEM should work with it… provided the antenna coupling is good enough.
I need to change the wording on this… it has nothing to do with the reader… it has to do with the inherent issues with the T5577 chip inside the xEM. There is no fixing it… it will always be a risk when writing changes to the xEM. https://forum.dangerousthings.com/t/quirks-of-the-t5577-cloning-tags-to-the-xem