I was able to test this today in Expedition.
Medusa's white skill lasts 7 seconds; mine has 165.9% longer disables so figure roughly 18.5 seconds before tenacity is applied.
Storm Drake's orange skill stuns for 6 seconds; mine has 6.3% longer disables so we'll just call that 6 seconds, lol.
Here is the video I got:
At the 0:20 mark (1:20 in fight time), he throws his stunning bolts. Watch Roller - she stays stunned until ~0:26 (1:14).
The second attempt I use Medusa's white instead. Her white hits Roller at ~0:51 (1:26 in fight time). Roller pops out at ~0:54 (1:23 fight time), just 3 seconds later.
The only logical conclusion is that tenacity is applied to Medusa's skill and not Storm Dragon's.