Details? Are these files RAW, NEF files or are they jpgs? Do you save as DNG or jpg or what? When you say "click on the SD card and import the selected images," do you go through the File>Import routine, drag the files to the Photos icon, or what?
You don't say-- have you restarted the Mac? Have you restarted in Safe Mode?
Start up your Mac in safe mode - Apple Support
Have you tried working in a different User account to see if the problem is in your User account?
Have you tried this with a new Library, to see if the Library is a problem?
Have you tried re-building the Library? --close Photos and re-launch by option-command-clicking the app icon. If you use iCloud Photos, it’s possible that this will cause a re-sync that lasts long enough to make you nervous.
As for my workflow: I use jpgs from my Z8 in Photos. When I decide to edit raw NEF files, I import them directly into Lightroom, export them as jpg, and then drag to Photos. I'll then have two versions in Photos and two, NEF & edited jpg, in Finder. I back up all of them.
When I edit jpgs in Lightroom, I use Edit With, and export as jpg to Finder. Again, I get two versions.
When I use the GraphicConverter's extension edit in Photos' Edit mode, I save, and then Photos asks if I want to save the changes. That happens immediately. Photos keeps the original, and it keeps the edited version to add more edits to later. So, again, there are two versions, though I see only one.
When I use Edit With Photomator, the picture automatically goes into the Library.
I haven't experienced the delayed reaction thing.