No such thing as a traditional Roth IRA. You either have a traditional IRA or a Roth IRA. In order for your 403(b) retirement funds to be not taxable, you need to roll them into a Traditional IRA.
A rollover is not a contribution. You would need to roll over the funds to a traditional IRA, then make a contribution after the rollover, to count as an IRA contribution.
See chart below.
https://www.irs.gov/pub/irs-tege/rollover_chart.pdf
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