Rasmussen claims that he is from the late 26th century and has traveled nearly 300 years back in time to meet the Enterprise. That would have taken him to the late 23rd century. The adventures of Picard & Co. however are set in the second half of the 24th century (around 2368), which is, at best, a little over 200 years before Rasmussen's alleged origin.
At the very beginning, Geordi says that they are already seeing "climactic" changes. Climactic changes are changes relating to a climax or tension point. What he means is that the planet is experiencing "climatic" changes, which are changes related to climate.
The Professor claims to be an historian from the future, and Picard seems to accept this, saying in the crew briefing that the Professor's credentials seem to be in order. It would arguably be rather difficult to verify the credentials of someone from the future, whose 'credentials' don't exist yet.