You're correct about the battle. Not sure why the various provincial regiments are included in that part of the catalog. It might have been better to have made a generic "French and Indian War" catalog for those.
Our own Pennsylvania Provincial Regiment didn't serve outside the colony, as far as I know. It was raised by the General Assembly to defend our own frontier, with the natural barrier of the Susquehanna River serving as a defensive line. We established a major fort, Fort Augusta, at the confluence of the North and West Branches of the Susquehanna (present-day Sunbury, PA), and smaller forts, outposts, really, south along the river to its mouth in the Chesapeake Bay. The regiment operated along this line, and into the back country of the Allegheny and Monongahela Rivers.
It's interesting to consider that the regiment had to be raised anew each year, with a new bill in the Assembly. The politics were complicated. Some Quakers were against raising any armed force; other Quakers supported it. And among the other English settlers, some were against any kind of standing force, others were for it. Masters wanted recompense for any indentured servants or apprentices who wanted to enlist. And the Penn family was against paying any taxes of any kind on their own properties (they eventually agreed to pay a special rate). Getting the regiment established at all was a real achievement.
Prost!
Brad