You should probably read the actual study. The journalist obviously understood it poorly and conveyed his confusion in his writing.
https://www.researchsquare.com/article/rs-558954/v1
Here, we present first molecular evidence that vector-based vaccines encoding the Spike protein exhibit a problem that is completely absent in mRNA-based vaccines. This is due to the fact that during the vaccination step, the adenoviral DNA enters the nucleus and use the host machinery to transcribe its (trans)genes inside the nucleus.
Oh, no, we can't do something like that - let facts and reality-based knowledge get in the way of a good false narrative?