They verified Linear B against a new tablet that turned up in a dig after the Kober/Ventris* solution had been published. It had pictures of jars with no or one or two handles, and the claimed Linear B for "two handled jar" and such next to the correct picture.

* Ventris' publication, but given Kober's contribution to the work they should really share equal credit. I like to think Kober would have got there on her own if she had access to the larger corpus that Ventris had (the Pylos tablets) and a comparable amount of free time and money available.

Linear A/B testing?

Yes, that's where it was shamelessly stolen from.

(Also: the passive voice was used.)

You look at the proposed sound values and compare it to other known languages. Languages from the same family share grammar and vocabulary.

I mean it's not like anyone could objectively go back in time and query ancient civilizations for what they meant, but presumably it means the verification heuristics, they have currently, pragmatic success, and expert solidarity means that it is "verified"

You can evaluate the logic for the decipherment step by step and make sure all the claims are justified. But the best test is to try the proposed decipherment against some new text and see if it makes sense. In the case of Linear A and the other remaining undeciphered scripts, there's not a lot of held-out text to test against, so it's tricky.