HOTween: Starting in the middle of a path

I've been trying to figure out how HOTween works, but so far the solution to this eludes me. The basic idea is I've got an object moving along a path. Nothing fancy, just moving from point A to point B, then it is destroyed at the end. At random points along this path, other objects are creating around this main one, and also need to move along the path.

The issue I'm having is that I can't figure out how to get these created objects to move from where they are instantiated to the next point on the path, and then continue on. Right now all I can work out is for the objects to, from their point of instantiation, move to the first way point and start the path from there.

The most straightforward way I can see this working is to get the waypoints that the first object has passed, and remove those from the waypoints of the crated objects, but I can't find a way to use HOTween to do such a thing.

Is there another tool I can use to get this effect?