Been testing the adapter on my A7 III and A6300, and it's mostly very, very good with the handful of lenses I have.
AF-S NIKKOR 28mm f/1.8G: AF as fast as on my D700. Extremely accurate except in quick moving subjects toward/away from camera. Needs a bit more contrast than native lenses to lock on. Excellent low light sensitivity.
AF-S NIKKOR 50mm f/1.8G: Same as above, though a bit of hesitation if it misses the target.
SP 70-300mm F/4-5.6 Di VC USD: Same as the 50, but only at 70mm. SUPER slow to lock on at any other focal length, but it does lock on just as accurately when it finally gets there. Not very usable unless you're shooting still subjects and don't mind waiting a few seconds for each shot. IBIS fights against its VC.
That said, this adapter, like nearly all others, isn't very usable for quick moving subjects on these cameras (might be better on stacked sensors), but 100% fine for things like landscape, product, and portrait work. One other thing to note is that it keeps the lens wide open full time, like on a DSLR. Not terrible, since you can assign a custom button for aperture preview if necessary.
My main need for the adapter is to keep the 28/1.8 after selling my D700. Love the lens, its sharpness across the frame, most of the bokeh (minus the LoCA), minimal field curvature, and the relatively light weight. Nothing much like it out there for FF in its price range (FE 28/2 bokeh is a bit busy). The other two lenses are being sold, and I'll probably pick up the Samyang 45/1.8 to replace the 50. Already have a Canon 55-250 STM and MC-11 to replace the Tamron.
A little update: just picked up an A7R II, and the lenses act roughly the same on it. The only difference is if you need to move the AF point outside of the OSPDAF area, you need to switch the AF system to Contrast Detect. This also forces AF-S, and runs very slowly, like how the Tamron 70-300 VC acted.