Firstly, yes it is true that this happened 26,000 years ago! More specifically, the event happened 26,000 years ago in our reference frame. There are other reference frames in which this event occurred two minutes ago or 5 million years ago. But generally these are not useful reference frames since the Earth's reference frame is not too different from the reference frame with respect to the center of mass of the Galaxy (we are not moving all that fast compared to the speed of light).
That said, as astronomers we are not particularly interested in dating precisely when the event happened. 26,000 years is a very long time in human history, but it's not very long on astronomical timescales. Not very much has changed in the Galaxy over the past 26,000 years, so we don't gain much by dating it at the time the event occurred (with respect to the Earth's reference frame, of course). Furthermore, we wouldn't even know exactly when it happened even if we wanted to! Our clocks are very precise here on Earth, but our distance measurements to most celestial objects are very fuzzy, particularly the further away you get. Because of this, these sorts of events are always referred to with respect to the year they were observed on Earth. (Thus, the most recent nearby supernova is known as 1987A because it was the first supernova observed in 1987.)
This all changes when you are studying more distant objects though! For very distant galaxies, we are now seeing things when the universe was considerably younger and things were much different. Then it becomes important to keep the event's age in mind. For these objects we will actually refer to their redshift. The redshift can be measured relatively well, and is related to the distance and age of the event via the Hubble constant and the acceleration parameter. Measuring these parameters is tricky and is a whole subfield of their own, so we usually stick with redshift as it is more related to things we can easily measure.
A final note on the paper itself. These observations were taken at Keck on Mauna Kea. There has been a lot of controversy around the construction of the Thirty Meter Telescope, so the authors actually acknowledge indigenous Hawaiians specifically in their paper:
> The authors wish to recognize that the summit of Maunakea has always held a very significant cultural role for the indigenous Hawaiian community. We are most fortunate to have the opportunity to observe from this mountain.