Power electronics-based three-stage smart transformers (ST) can be seriously damaged by inrush currents and overvoltages during the start-up phase if the control of the stages is not correctly coordinated. Hence, it is crucial to design properly the start-up procedure, especially in case of modular architectures with distributed DC-links. The design of the start-up procedure depends on the ST power stages topologies, their control systems and the operation modes. This work proposes a soft-shift start modulation technique that allows to limit the inrush current in the DC/DC isolation stage during the DC-link capacitors pre-charging. A fast voltage balancing control, performed by the DC/DC isolation stage, is introduced to avoid overvoltages and unbalanced voltage conditions among the different power cells. Under the proposed method, fast control dynamics is guaranteed thanks to the high frequency bandwidth of the DC/DC isolation stage converters. Theoretical analysis, based on a detailed small signal model of the ST, and simulations are used to demonstrate the principle of the operation. Experimental results, carried out in a ST prototype, confirm the performances of proposed solution in realizing a smooth start-up without voltage/current overshoots.