Most scented things are "activated" by heat.

I'm skeptical of the "all natural" claim to the scented materials, though. Essential oils dissipate pretty quickly. Absolutes dissipate even faster.

I would guess she uses fragrance oil, which is usually a mineral oil base with synthetic fragrance (typically derived from petroleum). The filling wouldn't matter that much, whether it's cotton batting, polyester, rope, sawdust, rice, dried herbs, or whatever.

Sew a tube of fabric, fill it with scented junk, roll it up, and either glue or sew it to secure it.

I'm not sure I understand the appeal of scented coasters, though. I'd imagine it'd interfere with the scent of what I was drinking. That's why people don't use scented candles on the dinner table.