Does anyone have any suggestions when you substitute brown sugar with turbinado sugar in rub recipes. What difference have you found in the results? I have never used it, but would like to start experimenting.

There is no meaningful difference in results. It's easier to work with though as it doesn't get hard or clumpy like brown sugar.

It's said to handle hot temps better but this is really a non-issue as typical cooktemps are not high enough to burn (or even caramelize) table sugar or standard brown sugar. Even high heat cooks (within reason) are not high enough to burn sugar though it will caramelize.

Isn't this turbinado sugar a fancy name for plain ole unrefined raw sugar ?

Kind of. It is partially refined.