While the code EE amount counts toward the amount used to calculate your Retirement Savings Contributions Credit, it is not a Roth IRA contribution (or any other kind of IRA contribution) and does not count toward your Roth IRA contribution maximum. A 457(b) is not an IRA.
A designated Roth account and Roth IRA are two different accounts. The amount in Box 12, Code EE counts towards your limits to the designated Roth account, however, not to your separate Roth IRA.
The amount on your W-2 does flow to your Retirement Savers Credit on TurboTax. However you have different contribution limits if you have a designated Roth account and a regular Roth account.
"Can I contribute the maximum, including catch-up contributions, to both a designated Roth account and a Roth IRA in the same year?
Yes. if you are age 50 or older, you can make a contribution of up to $24,500 to your 401(k), 403(b) or governmental 457(b) plan ($18,500 regular and $6,000 catch-up contributions) and $6,500 to a Roth IRA ($5,500 regular and $1,000 catch-up IRA contributions) for a total of $31,000 for 2018. " [From:https://www.irs.gov/retirement-plans/retirement-plans-faqs-on-designated-roth-accounts#5]