I took my 5* r3 venom into story quest 5.2.3 against the first classic spiderman. During the fight, spidey evaded several times; here's one example.

Venom's abilities text states that all spiderverse heroes' passive evades are shut down. This was not the case for this fight. Not sure if it's only happening in the story mode as I have not experienced this in other parts of the contest.