What does your setup code do? How is the circuit handling the inputs before setup has correctly configured pins? Does all this different powersupply include if the Arduino USB is connected or not? (this makes the timing for powerup change as the bootloader does some probing) How do you power the circuits (not the Arduino)?
And last but not at least : is this a real problem? Rephrasing: what would be wrong in supressing any sensor input for a short while (f.ex. the first round of the loop() ?) Having written that, I want to contradict myself by pointing out, that finding the root cause of any "suspicious" behaviour in a program or system is good. Ignoring or supressing it hides some other error, that may be worse.