Have you looked at the Tandem online ebook linked below? The book’s second chapter, Customizing Your Insulin Dose Setting, covers the settings you seem to be asking about. Perhaps it might help? (The chapter goes over some of the arithmetic I wave my hands at below.)
The approach I take to decide which setting to change is to test them separately.
The Correction Factor (CF) is only about correction boluses. It controls how much insulin to deliver to lower your BG by a given amount. Carbs should not be a factor when testing your CF settings.
To sanity check your Correction Factor, enter a correction bolus into your pump when your BG is at a stable elevated level and you haven’t eaten anything.
As the bolus takes effect you should see you BG drop back to your target BG setting. If your BG is not lowered enough, then your CF may be too high. The Correction Factor is just the amount your BG should drop for 1 unit of insulin. So if the CF is too large then the pump assumes less insulin is needed to lower your BG.
Similarly, if the Correction Factor is too low, then your BG will be lowered too much. You may need to consider increasing your CF.
The I:C ratio is about food boluses, not corrections. It specifies how many grams of carb one unit of insulin will cover.
To see how well your I:C ratio setting is working, wait until your Blood Glucose (BG) is steady at approximately your target BG. Then bolus for and eat a known amount of carb.
Your BG should go up, peak, and then come back down to your target BG. If your BG doesn’t return to your target BG but instead stays high, then your I:C may be too high. That is, the I:C setting indicates that 1 unit of insulin will cover more grams of carb than it actually does. So you may want to lower your I:C ratio slightly.
If instead your BG falls below your target BG, then your I:C ratio may be too low. That is, 1 unit of insulin will actually cover more grams of carb than your I:C settings says it will. You would want to think about raising your I:C level.