It can take weeks for putty to be ready to accept paint. If you apply the primer too soon the surface will ripple as you run the brush over it.
I am guessing that these are sliding sash windows- if yes, have you had new parting and staff beads with brush piles added? If the parting beads have brush piles, it massively increases painting time (in part because you do not want to get paint on the draught excluding brush pile).
You say that someone else has restored the windows. Have they gone back to bare timber where the sashes meet the the sash box? By that I mean, has the lower sash been sanded back to timber where the styles (read: vertical bits) meet the parting bead? Is the same true of the upper sash where it runs in the box?
Last year, I quoted just over £8k to paint sash windows on a house who's windows had been restored. Unfortunately, I didn't realise that that they had been restored over two years before. The sections of window that I referred to above had had one coat of DULUX Trade Weathershield preservative primer. Unfortunately, the edges of the old paint started lifting and I had to spend hours feathering the existing paint. I under quoted at least £2.5K (by the way it was a double fronted house with windows on 3 elevations).
I would strongly recommend that you ask the person restoring the windows to leave the parting beads and staff beads "lose" so that you can remove them each day whilst you paint the sashes. It is the only way that you will be able to undercoat edges that now only have primer. It also means that you do not need to worry about the paint on the sashes finding its way on to the brush piles as you slide the windows up and down.
I would estimate that it will save you at least 20% time wise, but it all depends on the quality of finish you are looking for. On the downside, either you or the restorer will need to hammer the staff and parting beads back, and caulk the exterior gap of the parting bead before painting the lower channel.
In an ideal world, if the property is large enough, I paint each of the two sashes. Allow a day for the paint to cure. Get them glossed up and then focus on the actual box. You do not want to pull the top sash down and scratch the paint in the lower channel.
