The booming personalized and customized demands of customers in Industry 4.0 pose a great challenge for manufacturing enterprises in terms of flexibility and responsiveness. Nowadays, many effective dynamic scheduling approaches have been proposed for manufacturing systems to quickly respond to changes in customer demands, where, however, the implementation of an automatic programming method with high control accuracy and low control delay is still challenging. The above unaddressed issue brings about a lot of labor-intensive and time-consuming manual offline programming work when adjusting the scheduling scheme to meet dynamic customer demands, resulting in limited flexibility and responsiveness in current manufacturing systems. To bridge this gap, a bi-level adaptive control architecture enabled by an automatic programming method is proposed and embedded into a digital twin manufacturing cell (DTMC). The bi-level architecture aims to automatically map an input task scheduling scheme with a batch of jobs into a group of control programs through a behavior model network and a set of event models embedded in DTMC. It also provides an adaptive program modification mechanism to quickly adapt to the dynamic adjustment of the scheduling scheme caused by the changing of customer demands or production conditions, thus equipping DTMC with strong flexibility and responsiveness. Based on the bi-level architecture, a DTMC prototype system is developed, where its application and evaluation examples demonstrate the feasibility and effectiveness of the proposed method.