Attaching stairs to sub floor

Not sure if this is the place for this but anyway...

I've ripped out a couple of walls and hand rails and are now finishing of around the stairs with floor boards that go over the edge of the stairs. The stairs are only supported by resting against the sub floor and via nails that have a 2" gap to bridge (and hence allow movement) I'm assuming that stairs are usually done this way to allow independent movment when expanding and contracting. Is this right? Would I be able to connect the stairs directly. They used to move and creak substantially (sliding against a vertical support) which I've largely eliminated with supports but it would be a lot easier if could just fill in the gaps with timbers and bolt/ glue it al together.

I'm not planning on nailing the floor boards to the stairs as I'm thinking even minor movement would split them (it's cypress as well) but I'm thinking of using some sort of gap filler/construction adhesive under them to provide support - there's a bit of a gap in places as the stairs aren't entirely square. I'm even considering using light smear of oil to prevent the adhesive fixing to the floor board too strongly. Is this reasonable or am I just making a problem out of nothing?

Time to post a pic I think...
Tools

Don't have a digital unfortunately. Not here anyway.

Not sure how else to describe it. The stairs don't have a top tread. And so the vertical of the last stair is what I'm resting the floor board on (I'm using ~130mm floor boards as edging). The stairs end at a 90 degree turn and so I have two sides on the top level - not that that really matters - except that it seems to have made the stairs somewhat less stable.

Well in the absense of any better advice I did a bit of both.

Screwed the stairs to the sub floor with largish holes in the stairs on only one side so that'll hopefully allow a little movement if it's required. Didn't attach the tread to the stairs but as there was a gap to fill packed it in places and used construction adhesive with glad wrap over it elsewhere for support. See how it goes.