I have a tandem that uses STI (Ultegra 9sp for the rear, Tiagra 4400 triple for the front) on Truvativ cranks and rings and the whole thing works very nicely. It was easy to set up, functioned correctly from the beginning and has never needed much fiddling to keep in good order. I have not used other STI triple shifters apart from this old used Tiagra unit, but it seems to have a bunch of stops and trim positions which allow one to always find a FD position that works. STI has a place on tandems. I am keen to try 10sp.
On the other hand my Scott (Dura Ace 7800 10sp groupset) came new with inline cable adjusters and until they were removed was always giving me the irrits. I would get everything - front and rear - working well but after an hour on the road gear changes would start to get sketchy and after 100km the chain would be nearly one gear behind at the back and would refuse to get onto the big ring no matter how hard I whaled on that left hand lever. That bike is now 40-50,000km old changes reliably when new cables etc are installed and correctly adjusted.
My experience is that inline barrel adjusters unwind due to road vibrations. Some unwind quickly, others take a week or a month or more. I have never had one that would stay set for any length of time. I think the ones I have used have been Shimanos, perhaps other brands (I think Jagwire do them too, for example) might be more reliable. Conversely I have never had a problem with conventional frame or derailleur mounted adjusters, regardless of the brand.
The front derailleur on a tandem is not much further away from the shifter than a rear derailleur on a single bike and we now expect to get 11sp working well on singles, it is reasonable to expect reliable changing on a tandem triple.
Anyway, post a picture of you and your stoker and the bike on the happy tandem couples thread sometime!