STAR to neighboring airport

Recently I was arriving from the southwest to my home base of UES (Waukesha,
WI), and was given the Veena arrival.

However, the Veena arrival is not listed as a STAR to Waukesha, but is under
the section for Milwaukee, which is around 20 miles away (in the Jepp
charts). Waukesha is not under the class C area of MKE. On the chart there
is no listed transition to Waukesha. However, one of the fixes on the star
is the Badger VOR, which is the IAF for several approaches into Waukesha.

There is also a nearby class C, which is Madison.

If unfamiliar, issuing a clearance with a STAR to a nearby airport might be
confusing. If suddenly going nordo where should one land- at the original
airport or follow the complete transition into the class C? (I know this is
a somewhat academic question)

Is this a common practice for controllers? I could see it producing some
confusion by pilots if unfamiliar with the area. Using NACO charts it is
easy to look up, but in the Jepps it could be very difficult to find.