First queens emerged 2015

[Jon]

The incubator is optional. I use it for convenience so I don't have to run up to an apiary to collect cells. I like to have some handy at alltimes.

That aside, forget about eggs as you graft with a small larva. The queen should be emerging 12 days later.
I find it useful to keep that 12 day period in my head. If you graft on a Thursday the queens will be emerging on a Tuesday.

There are two main ways to do this (a) putting a ripe queen cell into an apidea, (b) putting a virgin queen into an apidea.
Both methods work fine.

(a)With a ripe queen cell I fill the apidea with bees, insert the cell and open when the queen has emerged from the cell.
You can check if the queen has emerged by removing the cell from the hole in the inner cover of the apidea.
I put thecell in as late as possible before emergence which avoids any risk of chilling.

(b) With a virgin queen, the routine is slightly different. The virgin could be a few hours old up to several days old so that part is flexible.
You have your virgin queen ready in a roller cage and also a scoop of wet bees which you have prepared earlier Blue Peter style.
The virgin is shaken into the apidea and 2 seconds later the scoop of wet bees is dumped on top of her.
Apideas are filled through the floor which slides out.
The apidea is opened on the evening of the next day.

The queen can take a mating flight 6 days from emergence but depending upon the weather it could be 25 days from emergence.
There may be more than one mating flight, on the same day or over several days.
Egg laying usually starts 2-3 days after the last mating flight.

DR, I assume you mean 10 days from emergence not 10 days from the mating flight.

Cells from which a queen has emerged look like this:
emerged-cell-cap.jpg queen cells after queen emerged.jpg