My understanding with the Nicot system was that the Beek was to release the Queen after she had laid up the Cell Cups (say the next day) and then wait for three days for the eggs to hatch so that you have larvae of 1 to 24 hours old, these are then placed onto a Queen Rearing Frame. HOWEVER after experimenting with Nicot, I felt it would be best to transfer the EGGS and NOT wait for them to hatch into Larvae - in other words (it appears) to be the same as what is being advised in this video.
In my Grafting / Queen Rearing I have found best success is achieved by using a "Swarm Box" (I prefer the descriptive name Queen Rearing Box), basically a nuc with plenty of Nurse bees, a frame of pollen and a frame of open honey, and the queen rearing frame is lowered into the middle (just to be sure to be sure - check the frames 24 hours after you have made up this box to make sure there are no eggs in any of the cells, evidenced by Queen Cells being drawn out: I transfer the frames to be used above a Queen Excluder the week before... one bitten twice shy!). By transferring the EGGS to a Queen Rearing Box that is HOPELESSLY Queenless the nurse bees will be forced to care and raise the eggs in the Cell Cups into Queen Cells; it appears that the bees in a hive WITH plenty of eggs / larvae will often remove the eggs in the artificial Cell Cups.
The Nicot and the Jenter systems are basically the same, except that the Nicot is a simpler design and I think from inspecting the internal bases of the Cell Cups I think the Nicot is best designed.
Another couple of things that will help, never re-use Cell Cups (research shows this is best) and make sure that you apply quite a bit of pressure when you attach the cream/yellow coloured Holder to the back of the Cell Cup.
Hope this all helps you.