Piff 

Recently I purchased a Stronlight Delta headset, italian standards. It was to be a replacement on a bike that I recently successfully installed an 1" ISO headset. The ISO headset fit as expected, required all the usual tools to press the cups and place the race.

Strangely, the Stronglight headset did not require any tools to seat. The fit wasn't so loose that the cups/race slipped in/on, like an ISO headset into a JIS frame. It still required some effort, not much, to push the pieces into place. I have yet to go ahead and finish the installation.

Is this alright? I did still do a proper install of cups/race with the right tools. Maybe the stronglight headset was once installed

Again, it isn't downright 'loose'. Just looser than seems right. There is still an interference fit between the frame and the parts...but I'm worried something's off.

Thank you.

SurferRosa

I think you're all right as long as the pressed cups don't move when you try to turn them by hand.

One thing you could do is mark the cups with tape to see if they move after a ride (or several rides)