"You only pay when you sell" is not necessarily true. Some states tax the ordinary income if you own enough shares . But I agree with the other poster, usually there isn't enough income for the states to be concerned enough about.
For most investors you will not have to pay anything in another state. The income will be so low that you will not pay in a state where it is your only income. In my state there is no tax as this is partnership income except the part you file on the federal income tax from the K-1 is the only part taxed. If you keep the income small and you get $5 in a state here or there it might be exempt. The only problem is with the internet more states are looking for revenue and might find you. So I could be wrong. Some states try to tax IRA's and that can mean you pay over 100% tax which is what the AARP fought. So this might be a similar issue.
You had best have a talk with your CPA. You may have to pay state tax on your share partnership income earned in your home state even if shares held in IRA. MLP tax issues can get complicated,just let your accountant worry about it.