Connection does matter. Depending on the size photos you upload & speed. So if your connection is really slow, then it could take a few minutes. But only minutes for a few photos.
I retested this this morning. Using an 18 MB uVerse connection, it took 20 seconds to upload 6.1 MB of photos to the shared album. Showed both on the computer and iPhone at the same time. When I deleted them it was immediate on both devices. So for me, it is working much better this morning.
If you are using iCloud to store your photos, then it will probably be quicker.
Seems mine is working better now. What I did was to delete the shared albums and recreated a new one.
I also repaired my database since first trying. When you start Photos, hold the Command-Option key down and click Photos to start it. You will get the option to repair the Library. That may take out some of the kinks.