At least one of pressure pulses, lateral oscillations, and axial oscillations can be generated by a distal downhole tool and a proximal downhole tool while cement is pumped into a well for cementing the well. Also, the generation of at least one of pressure pulses, lateral oscillations, and axial oscillations by the proximal downhole tool can continue even when the cement is no longer pumped around a tubing and is curing. In order to do so, a backflow path from a point downstream of the second vibration tool toward a wellhead is provided. Then a fluid, usually other than cement, is pumped from the wellhead, through the proximal downhole tool, and back into an annulus toward the wellhead. As such, a production tubing may remain centralized while the cement is curing.