We're new to the tandem scene. We started with a set of SRAM twist shifters running 8 speeds on our Burley, and four months later we have drop bars and Ultegra brifters on a 9 speed cassette. Other folks have pointed out a few things for us which have been helpful.
My $0.02 worth
1) Tandem cables are longer than single bikes, so they stretch a bit more and it takes a little more time to shift.
2) As pointed out, anticipate and downshift early, or stuff like this can happen to you. Notice the bent big gear, one missing spoke, a kevlar replacement, and no cable to the rear D/R. Two people can generate enough power to bend a gear and really screw things up if something locks. We rode the last 11 miles of a charity ride using just the two smallest chain rings. It was a real learning experience. This was, I think, caused by trying to shift down in front and up in back just as we began to climb a hill, on a corner, at a real low speed.
3) Shift up in back before you shift down in front.
4) What type of front D/R is on your tandem? The SRAM front shifter on my Burley was a micro-index type, very akin to a bar end shifter, so it was very easy to put the D/R wherever it needed to be. If you have a "road" front D/R (Tiagra-105-Ultegra) it may not shift correctly with "mountain" thumb shifters due to the amount of cable pull.