AF-P won't work with your D90!
Like John says, it's the way(or type of) focus motor system in the
lens.
The last issue with the consumer dx model
lenses is if they are VR models too. I don't think any of the Dx VR
lenses have a VR on off switch!
Not only is this the second stupidest design choice of all time ... ever, it adds to the compatibility list above.
That is, you can't turn VR off if you don't have a camera that is fully compatible. The option to turn VR on/off is now an in camera item, not on
lens like the old days.
I think the firmware update for those listed cameras adds the VR option in the camera menu.
The Fx version of the 70-300 f/4.5-5.6 VR does have the VR on off switch, so isn't affected in this way.