From Jensen's point of view, signing this deal now insulates himself from a lot of risk. If he struggles adjusting to a new system or suffers a major injury, it could literally cost him 10's of millions of dollars. There's a value for Jensen in eliminating that risk, and that means the Caps can offer him less money in exchange for assuming that risk themselves. If they waited 20 games to see if he fits with the roster, his price would increase. Maybe it wouldn't skyrocket, but on a team that's constantly pressing as close to the cap as they can, saving even an extra 250K can make a huge difference.
There's also the psychological effect this will have on Jensen. Without a deal, Jensen would spend the next few weeks trying to adapt to a new club while knowing that his future earnings on his first big contract ebb and flow with every mistake he makes. We see pending UFAs struggle to find their game with new clubs with contracts on the line all the time. Signing this deal now takes that pressure off of Jensen, and sends a strong message about how confident the club is in him that they're willing to commit to him long term without a trial period. Maybe he checks out after getting his paycheck, but I'd bet that a guy who stuck with hockey and broke into the league so late is more likely to value that loyalty.