OK, so iOS 9 only refers to the phone. If you migrated to Photos on the Mac, then you are running either Yosemite or El Capitan.
So, when you say you turned off iCloud in your settings, do you mean you turned off iCloud Photo Library? What about My Photo Stream and iCloud Photo Sharing? These are all separate and very different functions, and the way you have them set up informs how you would proceed and how things act.
Based on what you have indicated, it sounds like you have iCloud Photo Library turned off (you wouldn't have a Camera Roll if it was turned on). So, in that case, your Camera Roll is your iPhone's Photo Library, and most albums (including Favorites, Selfies, Screenshots, etc.) are just pointing back to the original photo on the Camera Roll. So, if you delete a photo from the Camera Roll, it will also be deleted from the album.
Here are the exceptions to that rule:
Photo Stream is separate from your iPhone's Photo Library - it is a temporary stream that houses the last 30 days or 1000 photos that you have taken on your device. The primary purpose of the Photo Stream is to be able to share photos among devices that are signed on to the same iCloud account and that have Photo Stream turned on
Albums that you have sync'd to your device from your Mac are also not part of your iPhone's "Photo Library", so you cannot delete them directly from the phone. If you sync them to the phone from your Mac, you have to remove them the same way
You can turn on Photo Stream and iCloud Photo Sharing under Settings>iCloud and that will allow you to do several things:
1. When you have Photo Stream turned on on your device, and you are signed into the same iCloud account on your Mac, you can open the Photos app, and under Photos in the top menu bar, you will see the Preferences option. Click on Preferences, and under General, you will see an option under "Importing" to Copy Items to the Photos Library. If you check this option, then your Photo Stream photos (which are added to as you take photos) will be imported to your Photos library on your Mac automatically
2. When you have iCloud Photo Sharing turned on, you can select photos from your iPhone (or from your Mac) to send to other recipients in an album. This album will remain on iCloud until you remove it
The Photo Library on your Mac is what you see in the Photos app under "Photos". Albums that you see listed under the Photos are just like they are on the phone - they are folders where pointers are set up that point back to the Photo Library. So, you can delete photos from the albums and they will not be deleted from your Photo Library, but if you delete a photo from the Photos section, that photo will also be deleted from any album since there won't be anything to point to anymore once it is deleted from the source.
Take a look at the support links I posted to see if they clarify how you might want to use Photo Stream and Photo Sharing, and how you want to import your Camera Roll photos and videos to your Mac.
Cheers,
GB