It's a great question, James. Essentially, it takes three years of Major League service time for a player to reach arbitration eligibility and six years to reach free agency. A player acquires a year of service time when he remains on the Major League roster for at least 172 days of the 182-day season. Last summer, Fox Sports did a good overview here, which goes into some of the notable exceptions such as Super Twos.
To avoid a player reaching Super Two status (a year of extra arbitration eligibility), prospects with no MLB service time usually have to be kept down until mid to late June. This matters, because once a player hits arbitration, his salary usually jumps from the mid-hundred thousand dollars to at least the low millions. And of course, eventual free agency brings much bigger dollar figures and freedom to go to another team. That's why some teams choose to hold players, who are essentially Major League-ready, down in the minors for a few weeks or months: it stalls the clock from counting down towards arbitration eligibility, free agency, and - most importantly - a bigger pay days for young stars.
Of course, teams can't come straight out and say this - the Players Association would have legitimate gripe if they did. However, it's become pretty common practice. In the last few years, some of the more notable cases include Evan Longoria, Buster Posey, Bryce Harper, and even Ike Davis.
So as it pertains to Wheeler and d'Arnaud: Unless the Mets are painted into a corner (be it injuries or exceptional performance in camp) and they are left with little-to-no choice but to put them on the 25-man roster to start the season, they will likely hold them at Triple-A Las Vegas until late April/early May at the earliest. That way, like the Rays with Longoria, the Giants with Posey, the Nationals with Harper, and so on, it guarantees the player is under the team's control longer, and it puts off their eventual pay day, which means more financial flexibility in the short term.