It's a question of semantics. The OP is measuring the stem diameters, which equal the steerer IDs, while IthaDan is trying to explain the standard nomenclature for quill stems is by the OD of the steerer they fit. ia, a stem which measures 7/8" is called a 1" stem because it's for a 1" threaded fork. The OP needs a 1-1/8" stem (measures 1") for his tandem fork.
I don't know that anybody sells the adapter the OP needs, but it would have to be a 1" OD x 7/8" ID tube long enough to reach from the top of the headset to the bottom of the stem where the expansion happens. It would have to be split at the bottom so it could expand as the stem bolt is tightened.
The OP can go to the hardware store and see if he can find something with the right ID & OD, then fabricate the shim with a hacksaw. Otherwise hus best bet would be to return this stem and shop for a 1-1/8" stem.
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