A couple of things...

Read up on the theory of being a Project Coordinator, because that often has very specific responsibilities.

Secondly, someone on my team always thinks I'm a micromanager. It's unrelated to whether I am or not. I've had people file formal complaints against me, quite often, for being a "micromanager," but I've never been found "guilty" of that. They've been identified as "disgruntled employees."

What you describe is clearly not "micromanaging." You can tell them that's not what the word means. Micro-managing is directing someone to complete tasks in a certain order or process so that they cannot make up their own minds what to do at 10:30 and then 10:45am. It does not refer to requesting status.

Here's what I think is going on- 1-2 people are trying to push you around. You are nervous, because you're new. That way you don't know when to push back. You only take them seriously because you aren't confident enough.

Here's what I recommend- get status at the daily team status meeting- everyone in the same room talks- get the team, as a whole, to buy-in on what tasks are critical. Instead of saying, "Jack I need to know the status of Project A," ask "Jack, Phil needs to know if you've completed Step 2 because he's going to start Step 3 next."

But don't forget, if this team was EASY, they wouldn't have needed a Project Coordinator, they might just all be jerks