You’re trying to call a method taking a single string, rather than an array. Bear in mind that it’s the C# compiler which handles the params part, converting calling code which just specifies individual values into a call passing in an array. As far as the method itself is concerned, it’s just getting an array – and that’s what you’re mocking.
The compiler is actually turning your code into:
mock.Setup(m => m.GetFirstTicketInQueueIfMatches
(new string[] { It.IsAny<string>() }))
which isn’t what you want.
You should use:
mock.Setup(m => m.GetFirstTicketInQueueIfMatches(It.IsAny<string[]>()))
If you need to verify that it only gets given a single value, you’ll need to do that in the same way you would for a non-params parameter.
Basically, params only makes a difference to the C# compiler – not to moq.