I disagree. That is how they were characterized by the Catholics of the day, but where in Nestorian writings do we have evidence of this? I've not seen quotes from Nestorius to that effect in my books on church history. So basically we're trusting Nestorius' enemies for what he believed.Actually, no. The Nestorians were considered heretics because they separated the two natures of Jesus. Their objection to "Theotokos" was a by-product of this.
According to one church historian, the controversy started with Nestorius opposing the theotokos doctrine, and escalated from there. "Wishing to safeguard the true human nature of Christ against Apollinarianism, he attacked the use of the word theotokos (Mother of God), often applied to the Virgin Mary and up till then unquestioningly. God, he said, could not be born of a woman who could not bear a son older than herself, and the term implied that the human in Christ was swallowed up in the divinity" (A History of Heresy, by David Christie-Murray, 1976, p. 63).
Regardless of who's right on your point, my main point still stands that the Catholics have been Mariolators since the 5th century.