To be balanced you would hook it up like you described.
Cartridge + output to the non-inverted pin, the +.
Cartridge - output to the inverted, the -.
You might not have to use the ground pin, but if you do it should usually be hooked to the shielding on the cable. The proper place to connect the ground depends on the setup. Some will hum with no connection and some will not. I've had phono stages where I had to ground the spindle to stop the hum and some it made no difference. You will have to experiment with that.
Your dealer is correct in the sense that what you are doing now is probably not balanced. The adapters you have probably connect the + output of the cartridge to the balanced + and the - output of the cartridge to ground. That will work but it is not balanced.
You can get your own connectors, cut off the RCA connectors and wire it yourself. It is hard to do though because the wires are extremely small and very difficult to work with.
Cartridge + output to the non-inverted pin, the +.
Cartridge - output to the inverted, the -.
You might not have to use the ground pin, but if you do it should usually be hooked to the shielding on the cable. The proper place to connect the ground depends on the setup. Some will hum with no connection and some will not. I've had phono stages where I had to ground the spindle to stop the hum and some it made no difference. You will have to experiment with that.
Your dealer is correct in the sense that what you are doing now is probably not balanced. The adapters you have probably connect the + output of the cartridge to the balanced + and the - output of the cartridge to ground. That will work but it is not balanced.
You can get your own connectors, cut off the RCA connectors and wire it yourself. It is hard to do though because the wires are extremely small and very difficult to work with.