James Jones's weird contract saw the final three seasons guaranteed for only $1,856,000, $1,984,000 and $2,112,000 respectively, for a total of $5,920,000. If Miami cut him, that's all they would have owed him, a significantly lesser amounted than the $14,910,000 they would have owed him had they not waived him before July 1st. Miami tried to trade this contract so that they could owe him nothing at all, yet there were no takers, and so they ended up waiving him.
However, rather than paying Jones $5,920,000, they instead paid him only $4,920,000. In a bid to open up more cap room, Miami co-erced Jones into giving up a million dollars of what they owed him; they did this by agreeing to pay him what they owed him in one lump sum. The two most important rules with buyouts are that;
a) the amount of money that the team pays the player is that amount that is charged to the cap,
b) the amount that is charged to the cap is spread evenly amongst all remaining guaranteed compensation on the contract.
However, that doesn't affect how the money itself is paid out. Players and teams can pretty much do what they want in that regard. Put more simply, what you see on a team's salary cap chart (such as the one above) is not always what is actually paid out. Jones's incentive to give up $1 million was to turn three years of small checks into one big fat $5 million one that he could have instantly; Miami's incentive to cut him that check was to to reduce Jones's cap hit and open up more cap space. Using rule (a) above - whereby the distribution of the buyout amount must be equal to the distribution of guaranteed compensation in the original contract - Jones's cap hits became $1,544,172, $1,650,667 and $1,757,161 respectively, thereby opening up $311,828 in 2010 cap room for Miami.