Learning Fiore De Liberi

These wards are attitudinally ambiguous with regard to the line. You can hold (not referring to how you grip the sword) them rigid or loose with regard to the line.
Both di Dona for instance have an alternate form where the blade is pointing right down the line. Porta di Fero can be done with the blade anywhere in the front right between 12:30 and 3:00. The blade, in terms of where it is on the line, is fluid. It can be held on the line. It can be off the line.
The name is also suggestive I think. Pulsativa, pulsive or impulsive. A pump fake of the blade could be considered a pulse. If you just want to react to your opponent, that's impulsive. Again these types of things are dictated by the situation, and skill of all the fighters involved.