There is a flat side and a chamfered side to this tiny safety roller on the 16s Bunn Special.
I’m thinking the flat side butts up with the roller table. Leaving the chamfered side to face the lower pivot on the staff.

But why is it chamfered? I would almost bet that the chamfered side should face the table giving a bit more clearance on the pillar plate height.

My sense says putting it on the wrong way might lead to a cracked safety roller.

I am interested in the answer.
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You are just fine watching as an answer eventually will arrive. Saying so is also fine!

To my knowledge our posts are not automatically given email notifications and that would mean
Posters with hopes of replies need to keep a watchful eye......

I should always look beneath any part removed checking for proper orientation. Also too heavy a hit will crack these fragile tables.

Dumbness of me? I tend to find a way that helps start these 'accidents'.

Are you referring to the roller jewel or the smaller of the rollers in a double roller escapement?

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Yes. The tiny safety roller.
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OK...Short answer is concave side (chamfered) is out (visible).

I then should assume the purpose is the chamfer makes enough room
For end shake.

No...has nothing to do with end shake.