Wood – How to glue back a piece of wood (particle board) that fell from the kitchen cupboard

I'd go with an epoxy filler rather than a cellulose based product. You've already got chipboard, and you need all the additional strength you can get. Drill the old holes out to a size larger than the screws, including thread. Fill the holes with a 2 part epoxy and let dry. Level the surface as needed, then drill pilot holes for the screws into the epoxy. Screw the hinges back on.

Open Time

"Open time" is used in two different ways. For contact cements, it is the minimum or optimum time to leave the glue exposed before joining the pieces, because you want the adhesive to partially dry first. For wood glue and most other adhesives, it's the maximum time before joining the pieces because the surface starts to dry or cure and bonding degrades.

Working Time

"Working time" is how long you can reposition the pieces after you join them without affecting the ultimate bond.

Working time is often different from open time. With many adhesives like wood glue, you depend on the glue being very liquid to absorb into the material surface. However, the glue will bond with more of itself even after it has started to dry a little. So once the glue is adhered to the wood, you have a longer period in which you can move the parts around.

For some wood joining, this characteristic is used for stronger joints, especially on larger areas. A thin layer of glue is applied to both pieces, which starts to absorb into, and bond with, the wood surface. This allows more to be absorbed than might be the case if you immediately clamped the pieces and squeezed out most of the glue. While the glue is still in its working time, another layer of glue is applied to one of the surfaces and the pieces are joined. The second layer is in contact with glue rather than wood, so water (or other solvent) isn't being sucked into the wood, and that provides more working time. The solvent in the additional layer also extends the working time of the first layer.