I am guessing here. Icom changed the PTT circuit at some point. The signal from the tuner to the radio needs to be a ground. In the past, it was a +12V.
If you are using an older design tuner, it may place a 12V on the tune command lead. This has two effects – it may or may not cause the radio to start a tuning cycle, and the radio will report an over-temperature condition. This is because the radio has +8Vdc pull-up on that line that is also part of the thermocouple and by inserting 12Vdc the radio thinks it is running hot.
Icom tuners, and the IT-100 from LDG, correctly place a ground on that lead. Others may not. If your MFJ has an option to place a low/ground instead of a high/12Vdc on the control lead from the tuner to the radio, the whole setup may work better.