After the new product launched, orders came pouring in.
Tips
history
Traced to Zhu Xi's 《答何叔京》 (Song): 事物纷至而沓来 - events crowding in one on top of another. 沓 (tà) means 'stacking/repeating', intensifying the sense of unbroken arrival.
register
Literary and formal. In speech you'd more often say 接二连三 or 一个接一个. 纷至沓来 belongs in newspapers, reports, and writing.
