Aren't drivers supposed to safely pull to the side when they observe police cars approaching with flashing lights?

I don’t see this done much anymore and I’m beginning to believe the rules have changed and I missed the memo.

I was a few blocks from my home last week when I glanced in my rear view mirror and saw flashing blue lights (police car) two cars behind me.

I pull over.
The car behind me pulls over.
The police car pulls over behind us both.

We sit for maybe three minutes.

Then the police directs a search light to my driver side mirror.

We sit.

Finally, police approach from both sides of my vehicle, shine a flashlight inside and ask if everything is alright.

“Yessir.”

Why are you just sitting here?

“Uh…you turned the flashy light thing on.”

We were pulling over the car behind you.

“Oh…thank you Officer.”

I never knew you were supposed to first determine why the flashing lights were on. I just thought you were supposed to pull over.

What am I missing here?