Neither TurboTax nor your tax return classifies an RMD as applying to any particular year. Your tax return simply reports distributions. Any RMD (or any other regular distribution) received in 2019 is taxable on your 2019 tax return, regardless of the year for which the RMD was taken.
If you somehow mistakenly reported this distribution on your 2018 tax return, amend your 2018 tax return to remove it.
And hopefully you also took your 2019 RMD by Dec 31. So you might have two1099R unless they included both RMD on the same 1099R. Did the plan know it was for your 2018 RMD? They might think it was for 2019.
Yes, the institution knew part was for 2018, but they said they are bound by law to report all 2019 distributions on 1099-R
Yes, they knew it was partly the RMD for 2018 but said they were obligated to report all 2019 distributions on the 2019 1099-R.
My 2018 showed income greater than the 1099-R showed.
I'm wondering if the IRS will recognize that if the 2019 return shows under reporting the 1099-R by the same amount.
No, you can't do that. It was improper and a mistake to report on your 2018 the 2018 RMD received in 2019. If you did so you must amend your 2018 tax return to remove that extraneous income and report it properly on your 2019 tax return. If the 2018 RMD was a late RMD because the deadline for taking it was December 31, 2018, your amendment must include 2018 Form 5329 and explanation requesting waiver of the 50% excess-accumulation penalty.