Tiagra Rear Derailleur Compatibility
Is this because the parts are incompatible?

Yes. As groupsets with greater number of sprockets in the cassette were developed, the sprockets were spaced closer together to fit them in the space available. 11 speed road cassettes are slightly wider than 10 speed but the sprockets are still closer.
The chains for 8, 9, 10 and 11 speed groupsets are also not interchangeable. The chains get progressively narrower to work with the closer sprocket spacing.
What you'll need to do is mount a 10 speed cassette on the trainer. A small spacer is needed to deal with the slightly narrower 10 speed cassette on an 11 speed compatible freehub body.