State tax filing

You are correct. If the K-1 represents income received while only living in Virginia from January through June, then it would be only taxable to Virginia. You have to adjust the allocated income on each state return so that the additional income is taxed properly. 

First, complete the allocation on your Virginia return.

1. Open your Virginia return. 
2. Continue through the screens until you reach the screen, Part-Year Allocation, for Rent and royalty income. Enter the amount of K-1 income sourced in Virginia. 
3. Continue through the return.

Next, complete the allocation on your Delaware return.

1. Open your Delaware return.
2. Continue through the screens until you reach Delaware Source Income. Enter 0 next to Rent, Royalties, K-1s. 

I completed a mock return with a sample K-1 in the amount of $20,000. My 760PY showed the amount in taxable income and Form PIT-NON showed $0 as sourced to Delaware. See the allocation screenshots below. 

@MHiggs1