It seems my concept of the photographic process was wrong.
No. Incomplete maybe, but not wrong.
Shooting slide film (or digital jpeg's like your iPhone provides) you generally get a direct correlation of exposure to output. You are creating an essentially finished, usable product, defined by the camera's exposure and a standardized process that follows. (Yes the result can be tweaked but for clarity I'll skip that here.)
Shooting to get a specific result is actually the preferred method, you are trying to do what Ansel Adams and many others have taught. But there's more than one way to skin a cat and Ansel had control of every step in his process.
Negatives are a different animal than slides and jpeg's, they are just an intermediate step that carries a lot more info than normally will get printed.
To get finished output from a negative you have to "take a picture" of the negative, and to get finished output print exposure needs to be adjusted and print exposure is the variable that defines how bright or dark the print becomes. (Enlargers are nothing more than specialized cameras designed to control exposure when taking pictures of negatives. If you sent your negative film to a lab they might even use another specialized type of camera called a scanner.)
Practical example.
The disposable cameras that you can get at the supermarket don't have the ability to change exposure settings. Instead they use negative films and a fixed exposure setting. Some frames may receive a lot of exposure, others much less; regardless, all of those shots can be printed to normal snapshot brightness or to the dramatic brightness level you prefer.
For negatives, there is no direct, absolute, or even normal connection between camera exposure and final output.
The person printing makes that choice, or in a lab that choice might be made by some software.
This second exposure choice allows us lots of flexibility but it also mandates that we make a choice, choosing once at the camera isn't enough.
For your negatives that were printed too bright, someone or something made the choice to print them that way. All you have to do to fix that problem is tell the printer what you want and print again.
You have to make that choice, if you simply underexpose and don't tell to processor what you want, they will try and fix your "mistake" and the result still won't be what you want.