This is a difficult one to test, as there isn't an easy way to record critical hits and it deals with chances. However, I tried testing comparing Solar (melee), Vortex (ranged) and Nebula (magic - control) armour, plus no armour at all. (No accessories modifying critical hit chance equipped.)
The SD Fury's secondary attack is definitely using melee damage modifiers. Vortex, Nebula and no armour had no difference in damage.
Based on my observations, the SD Fury's secondary attack is also using melee critical strike modifiers too. Solar armour had a noticeably increased chance of critical hits compared to Vortex, Nebula and no armour.
Is there anything in particular that indicates it's using the ranged critical modifier that I may have missed?