Say you have a buy signal that does this: "If today's open > yesterday's high, then buy on open." What if this is triggered on the day after a rollover day? Is "yesterday's high" the high for the old contract or the new contract? What if using one generates a buy signal but using the other doens't generate a signal? I have read about using back adjusted contracts when doing backtesting. That implies you should use the old contract for "yesterday's high." This seems strange because you are effectively using the high of another contract to determing the buy signal for the contract you're trading. Now I know it's the same underlying, but in a system where your are looking for behavior from one day to the next, shouldn't you use the same contract? If using the old contract is okay to use, then why not just use the underlying cash market instead?
"Should" is a dangerous word, it implies that one course of action is correct in all circumstances for all people. Except when *I* use the world should I think you should program a computer to test all of the possibilities that you mention, and see which one you like best. Who knows? Maybe one of the options is TONS more profitable than all the others. Or, perhaps, the tests will show negligible differences among all candidates, and you can't go wrong no matter what you do. So flip a coin and be happy.