(whatever your name still is),
Your reader is behaving in the same way that a MOD-RFID125 does, not like a MOD-RFID1356. That is the source of the incompatibility with JMRI, as JMRI source code does not support the MOD-RFID125.
If you wish to have JMRI modified to support the MOD-RFID125, you may file an "issue" at github, as suggested by Dave H.
In the issue you file, please request the addition of support for the Olimex MOD-RFID125. Please include the monitor log information which you included in your original post here. If there are any errors reported in the JMRI "Console log", please include it. And please attach a copy of the MOD-RFID125 manual to the "issue".
Regards,
Billybob