dropped in D

I recently made a flight from Sumter, SC (SMS) to Columbia Metro
(CAE). Just after takeoff from Sumter, I contacted Shaw AFB approach,
told the controller that I was going to Columbia Metro, and got flight
following. Between Shaw class C airspace and Columbia class C
airspace there is Mc Entire ANGS class D airspace. As I approached Mc
Entire airspace, I figured that I was OK to enter because I had
established two-way communications with Shaw approach. After I got in
the middle of Mc Entire class D airspace, Shaw approach gave me "radar
services terminated, squawk VFR, for further flight following suggest
you contact Columbia approach on 133.4". Hmmmm.... Doesn't this mean
that the instant after he terminated me, that I was not in two-way
communication with the ATC facility (and unintentionally in violation
of 91.129(c)(1))? If so, what action should I have taken? Honestly,
I would have expected a handoff to either the Mc Entire tower
controller or to the Columbia approach controller, as opposed to a
"...suggest you contact...".

Also, 91.129(d) says "Each person who operates an aircraft in a class
D airspace area must maintain two-way radio communications with the
ATC facility having jurisdiction over that area." Where is "..the ATC
facility having jurisdiction over that area" defined? For example,
for the Mc Entire class D airspace, is this just the Mc Entire tower,
or do Shaw approach and Columbia approach also have jurisdiction over
that area? And if it is only the tower, then why didn't Shaw approach
hand me off to the Mc Entire tower prior to my entering the Mc Entire
class D airspace? (Note that the Shaw controller did not sound busy
and my flight path was such that it should have been obvious that I
was going through.)

Sorry for so many questions... I just want to do things 100% right
(well at least 90% of the time :-) )!

Arden