State tax filing

@nera I just had my first paycheck in a new job (where I work in DC and live in VA).  Payroll sent the majority of my state tax to DC and only sent a very small amount to VA.  Based on your comment about reciprocal state taxes and only needing to file in VA,… (1) should any $ at all be coming out of my paycheck for DC taxes?   (2) does a reciprocal state tax mean I will only realistically pay VA state tax level(~5%) or DC level (~8%) or some combo in between?