Thorncaster Sliver and Venom Sliver vs. Priority or Lack Thereof
The simple answer is that your opponent cannot use any of the abilities from Thorncaster Sliver to deal damage to Ethersworn Shieldmage, and Ethersworn Shieldmage can protect all of your artifact creatures from all of the damage.

This is the exact sequence of events for how your example should play out:


Your opponent declares 5 Slivers as attackers, with both Thorncaster Sliver and Venom Sliver on the battlefield.
For each attacking Sliver, your opponent puts their triggered ability from Thorncaster Sliver on the stack. This is part 508.2 of the Declare Attackers step. At this time, your opponent declares which creature each ability is targeting (see rule 603.3d and rule 601.2c).
Your opponent gains priority (rule 508.3). From how you described your example, they choose to do nothing and pass priority.
You gain priority. At this time, you cast Ethersworn Shieldmage.
You gain priority again, but you have nothing else to do here so you pass priority.
Your opponent gains priority. They have an opportunity to act here, but they can't do anything with the abilities from Thorncaster Sliver, because those are already on the stack. Once you do nothing and pass priority, Ethersworn Shieldmage resolves and enters the battlefield. At this time, the Shieldmage's ability triggers, and goes on the stack.
Your opponent has another chance to act, but they still can't do anything with the abilities from Thorncaster Sliver. They pass priority, and so do you.
Ethersworn Shieldmage's ability resolves. For the rest of the turn, any damage that would be dealt to any artifact creature is prevented.
The abilities from Thorncaster Sliver resolve. All of the damage that they would do to artifact creatures is prevented.


Your opponent did one major thing incorrectly: they tried to deal damage to the Master Transmuter in response to you casting Ethersworn Shieldmage. You didn't have an opportunity to cast Ethersworn Shieldmage until after all of those abilities were on the stack, so there is nothing they could have done to make one of those ablities resolve before Ethersworn Shieldmage.

However, since you revealed the Ethersworn Shieldmage out of turn, it would have been reasonable for your opponent to choose non-artifact creatures as the targets for any abilities that they had not yet declared targets for.