You're referring to "Rule #1: Don't Touch Anything", part of the TimeJumpers series of books by James Valentine.
The first and only rule of time travel in the year fifteen billion and
seventy-three is simple enough: DON'T TOUCH ANYTHING. Theodore Pine
Four is perfectly willing to follow this rule when he wins a contest
for the latest TimeMaster JumpMan. If all goes according to plan, this
new model should send him -- as an invisible onlooker -- to an
exciting time and place for a five-minute test-run. But instead of
landing somewhere cool, like the fall of Troy or the sinking of the
Titanic, why does he end up in the middle of some girl's bedroom in
the twenty-first century, where nothing interesting is happening?
Farah offers some additional info in her review here:
Jules and Gen, two teens, are the in the room in which Theo
materialises, and who need to keep him occupied at the same time as
they sort out their own problems. While Theo works out how to get the
co-ordinates to go home, they jump with him to different times,
including the First Fish, and the Last Whale. Eventually, when Theo
falls sick, Jules jumps forward to bring back his parents.