Residency vs state I’m currently employed in

Yes.  Your employer should withhold taxes for both states.

All income an Iowa resident earns is taxable to Iowa to the same extent that it is taxable on the federal return even if the income was earned in another state, local jurisdiction in another state, or foreign country.

If another state, local jurisdiction in another state, or foreign country taxes that same income, then the Iowa resident may be able to claim a credit on this line. Use form IA 130 to compute the Out-of-State Tax Credit.

Iowa Department of Revenue - Out of State  Tax Credit

If you are a part-year resident or nonresident, you must file if your Minnesota gross income meets the state's minimum filing requirement.  ($13,825 Single; $27,650 Married Filing Jointly, etc.)

Minnesota Department of Revenue - Who Must File an Income Tax Return