I did a test: on sandbox scenario I put 50 iron chest in an active provider chest. I also added a storage chest and a roboport with 100 robots.
you can find the savegame here (it is at 0.25 speed so you can see it in action easily - simply put the 50 iron chest into the active provider chest)
- 14 robots immediately departed to move them into storage chest (14 robots x 4 items/robot = 56 items) - "pickup" tooltip = 56
- Count of iron chest in "logistic system storage" tooltip becomes negative (50 - 56 = -6)
- when robots reached the active provider chest they recognized that 14 robots are too many, and only 13 are needed to transport 50 items (13 x 4 = 52) so 1 robot returned home (it should not have been dispatched at all)
- while transporting items, count is now 0 and "deliver" tooltip shows 50.
- While robots unload into chest, "logistic system storage" tooltip increase steadely, as soon a every robot unload.
- "logistic system storage" tooltip always 50, since items are moving to a storage chest and so they will be available to the network in few seconds. Of course it should not happen if they are instead moving to a requester chest.
- in any case no negative value displayed
- "right" number of robots dispatched since the beginning (13, not 14 and then 13)