It is the case that he returns from the remote past to the twentieth century and also that he becomes active in the twentieth century after the events of this Annual. However, his return was not by time travel but "the hard way," encased in amber, until John Constantine found and released him. It follows that, during the events of the Annual, he was not traveling through time but enduring in amber.
When an author like Gaiman writes a few stories set in a particular comic book universe, it is possible for him to create a mini-canon with its own internal references and background information. Thus, Gaiman's Swamp Thing short story, first published in Midnight Days, introduces the seventeenth century plant elemental, Jack in the Green, and it is this same Jack that conveys a message from the Parliament of Trees (retired elementals) to Abby in the Annual story. Gaiman also connected Poison Ivy, Black Orchid and Swamp Thing and that connection would have continued if he had become a regular Swamp Thing writer:
"If I'd written Swamp Thing this story [at the end of the Annual] would have set up for a huge and strange storyline, that has, instead, found its home in the comic boxes in Lucien's Library, I'm afraid. It began with the Wolves of the Woods padding out of the forests, thorns on their feet instead of claws..." (p. 16)
I have no idea how that story could have continued but I am not an imaginative writer. It is good to be told something about these unrealized narratives. The time traveling elemental would have met Jesus, a powerful white magician, then Gaiman and Jamie Delano would have succeeded Rick Veitch as regular scripters.