You're only requirement is to be speaking with ATC. Approach/Center is ATC.
And that's all well and good on an IFR flight. I've been on, and heard horror stories about, people getting flight following VFR and getting dumped into their destination's D airspace without approach letting tower know you're on your way. Two examples:
Approaching MYF from the north (have a look at the sectional if you've never been there), we had overflown Miramar, at which point approach told us to proceed direct to MYF and descend to 1500 ft, and told us "crossing the highway, contact tower." I had assumed that they had at least told tower we were coming. Imagine our surprise when we contacted tower, only to have them give about 4 traffic alerts and a very unenthusiastic "approach doesn't tell us anything". We didn't bust the D, since we had two way comms before/when we entered, but since there's only about a mile between the highway and the runway, approach had put us against crosswind leg at pattern altitude. Not a good place to be when you've just surprised tower.
I've heard a horror story about here at OJC, too. A guy was doing VFR practice approaches with flight following, and on their first one into OJC, approach didn't give them the switch until they were on a two mile final. The pilot got chewed out by tower, including threats of violation.
Finally, 91.129 says two way communication must be established "with
the ATC facility providing air traffic services," which in the case of D is tower. I just like to cover my own butt when I can and contact them on a second radio. It's more difficult with a two person crew, because to do so I have to tell the radio man how to do his job, which is something they understandably don't approve of.