My experience is a roll over is type of distribution. It would be reported as such to IRS and could be picked up by your Turbo Tax account. It doesn't mean it would be taxable. Typically a direct roll over from one qualified plan to another would not generate tax until withdrawn from the new account. When you walk through Turbo Tax steps for income you will have an opportunity to explain how you directed the roll over (distribution) to another account and did not receive it directly. However, I am not sure how or what you mean it would affect your saver's credit.
As far as these 2 rollovers, nothing gets entered in the contribution of an IRA for these two transactions.
If you received a 1099R for the two rollovers, both need to be reflected in TurboTax. Each will be reported separately and as long as it is from one Roth IRA to another Roth IRA there is no tax impact on the return.
To enter pension and annuity Payments (1099-R)
Each 1099R will be entered exactly as received in TurboTax, then answer the questions that follow and then enter the 2nd 1099R.
After the 1099R is entered, you will then answer some questions regarding it. You will answer that 100% of this was rolled over to same or similar account.