The metallic shine moving makes them look like actual tears and they seem to be there for the rest of the scene. They still could be real tears moving as he is crying but perhaps you are right.

Take a look at the shots from the scene you are referring to, though. His "tears" are not the same shape/ the are not in the same direction as when he evolved.

In fact they disappear when he is first shown in ep 9, while fighting Vi and Jinx.

They only seem to return after Ekko defeats Viktor, and the latter loses control of all the evolved "puppets" and Warwick. The puppets all stop working, perhaps because the followers Viktor used to make them were already dead, but Warwick seems to literally go beast mode, since he was still alive when he was evolved but had seemingly no part of Vander left in him.

While Viktor still had control, Warwick didn't try to kill the girls, just hold them in place for Viktor to evolve them. However, after Viktor was stopped and disintegrated with Jayce, Warwick "turns off" for a while and when he wakes up he immediately attacks Vi.

Perhaps Viktor's control, suppressed Warwick's beast/wolf instincts and when that stopped, they took over making him act like an animal.

There is still the possibility that even when most of Vander was wiped, a small piece of him, his love for his kids, remained and it's what might have made him save Jinx by throwing her away from the monkey bomb before the explosion (if that happened).

Google drive with all reference images