String comparison problem
As @timemage stated, strcmp returns 0 for equal. Sincerely in the provided code, while you send a message, which contents are not COMMAND, the LED will be turned on.
To get what we need, we must compare strcmp return value with 0! If it equals, then the strings match, and your suggested code is being executed:
void stringCallback(char *myString)
{
  if (strcmp(myString, &quot;COMMAND&quot;) == 0) {
    digitalWrite(13, HIGH);
  }
  Firmata.sendString(myString);
}