'Add image to photos' not working properly

I've just switched from an iMac to a MacBook Pro and am still trying to find my way round.

My problem is that when I want to save an image from Safari to Photos, I right click the image and hit 'Add image to photos.' When I go to Photos the image is there in the 'Recents' tab but it's not in the 'Photos' tab, and it's also not there when I go to upload the photo to the web (through Twitter or a web form, say).

I never had this issue with my iMac so I'm not sure what I'm doing wrong. One thing I notice is that on my iMac what used to happen is when I added an image the Photos icon on the dock would bounce to show a new photo. But now when I add an image from Safari what happens is the Safari window goes gray, to show it's been deselected, and there's no Photo icon bounce. Is this a clue as to what's going wrong?

As always, any help would be greatly appreciated. Thx