Well Yuri would have had relation with Tiberium series if Westwood would have made their own C&C 3 called Command & Conquer: Tiberian Incursion.
From C&C wiki from article Command & Conquer: Tiberian Incursion :
"...During the fighting GDI inadvertently activated technology from Command & Conquer: Red Alert in one of the vaults, including a Chronosphere. A chrono vortex threw Yuri back in time. Yuri was the result of Nod's psychic experimentations and an acolyte of Kane... "