Yes, I remove some ceiling tiles. I go for hot spots, under exterior doors, deck connections and under plumbing.
In my report, I state just what I did. Though not required by my SOP, I lifted a few ceiling tiles here, here and here then my observations and limitations.
You quite simply cannot determine it visually.
The age of the building is a clue, but only a clue.
My local lab charges $45 to look at a sample under a microscope and determine the asbestos content (if any).
The back of the ceiling tile MAY, but probably does NOT indicate who made it and when.