This wouldn't matter. The clients he's referring to will pester every day for ETAs even if you provide precise date/time ETAs at the time of order placement.

This behavior, among others, drove me to no longer do business with offshore firms.

Unfortunately, Darren, there really isn't a way to "deal" with this annoying behavior. Offshore firms, and some onshore, simply will not stop pestering providers every day on every order no matter how frustrating and counterproductive it is.