If the UL Wall Design (assembly) does not specify that the fire resistance-rating is from interior or exterior, does that mean it is rated for fire exposure from both sides?
Yes. That information is covered in the BXUV.GuideInfo – Fire-resistance Ratings – ANSI/UL 263.
Specifically in section VI. WALLS AND PARTITIONS of that guide, where it states that the ratings for walls and partitions apply when either face of the assembly is exposed to the fire unless indicated otherwise in a specific design.