A/B testing is widely used in the internet industry. For online marketplaces (such as advertising markets), standard approaches to A/B testing may lead to biased results when buyers have budget constraints, as budget consumption in one arm of the experiment impacts performance of the other arm. This is often addressed using a budget-split design. Yet such splitting may degrade statistical performance as budgets become too small in each arm. We propose a parallel budget-controlled A/B testing design where we use market segmentation to identify submarkets in the larger market, and we run parallel budget-split experiments in each submarket. We demonstrate the effectiveness of this approach on real experiments on advertising markets at Meta. Then, we formally study interference that derives from such experimental designs, using the first-price pacing equilibrium framework as our model of market equilibration. We propose a debiased surrogate that eliminates the first-order bias of FPPE, and derive a plug-in estimator for the surrogate and establish its asymptotic normality. We then provide an estimation procedure for submarket parallel budget-controlled A/B tests. Finally, we present numerical examples on semi-synthetic data, confirming that the debiasing technique achieves the desired coverage properties.