How do they know the mice have tinnitus I wonder? To find out if a person has tinnitus you have to ask them in a language they understand.
I think they attempt to induce tinnitus by exposing the mouse to a loud sound. Subsequently, they use a "gap detection test," where another sound is played which has a "gap of silence" in it. The mice have been trained to react to the gap of silence in some way (e.g. they stop licking water). Normal mice will react to the gap of silence as they were trained, but mice with tinnitus will not - presumably because the gap of silence is "filled" by the sound of their tinnitus. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4478067/
Tinnitus does not stop you noticing gaps in other sounds - I know because I have tinnitus. It seems more likely the mice do not notice the gap because they cannot hear well enough!
They may not have been trained to react to the absence of the sound created by the gap, but rather to react to total silence - something they couldn't experience with tinnitus. I did wonder, though, how they could be certain that the mice weren't simply deaf.
There's a full description in the methods section - Behavioral test of tinnitus with an acoustic startle reflex-based gap detection paradigm