I have two pieces of advice for you. The first is that you need to balance two guiding principles:
Start small and add on as needed, not vice versa.
Your workflow should reflect your reality.
I'm assuming you already have a pretty solid grasp on those, so I'll move on to my second piece of advice:
Ask the team.
While I know you didn't mention Scrum, its ...
It depends. Who's going to look at your boards, and why?
You should use Jira to meet your business needs and processes, not the other way around. So ask yourself and others:
Do we need to track both?
Is there anyone who cares about dev tasks but not management tasks?
Is there anyone who cares about management tasks but not dev tasks?
Is there anyone who ...
Short answer - yes, in your filter you will have items watched by other people so long you are also one of watchers. If you'd like to have a filter where you are the unique watcher, you'd need to also add an exclusion criteria stating that others are not watchers (which is cumbersome and not very effective).
Now, bringing the question to the PM / leadership ...