Springing on someone is a phrase that denotes a sudden act of surprise, assault or presentation of an idea or information. The antonyms for the word springing on would be calm or gradual. Instead of surprising or shocking someone, a person can gradually introduce their ideas or plans. The word 'gradual' indicates that the process is slow, subtle and peaceful. On the other hand, 'calm' means steady and composed, without causing any agitation or nervousness. These antonyms can be used to describe a more patient, methodical and strategic approach towards communicating with someone, without any abruptness or impulsiveness.