How does the NBA get paid by the networks for playoff games?

The NBA included rights to broadcast playoff games in the $24 billion extension signed with Disney/ESPN and TNT. This deal covers both regular season and playoff games:

Under this arrangement, ESPN will pay $1.4 billion per year, while Turner will pay $1.2 billion, according to Sports Business Journal.

Per the league's press release:

The National Basketball Association (NBA) has expanded its partnerships with Turner Broadcasting System, Inc. and The Walt Disney Company through new, nine-year agreements under which ABC, TNT, and ESPN will televise NBA games beginning with the 2016-17 season and running through the 2024-25 season

Quote regarding TNT playoff games:

TNT will televise up to 45 playoff games during the first two rounds and will have exclusive coverage of the conference semifinals games it telecasts and one of the conference finals each year.

Quotes regarding ABC/ESPN playoff games:

The postseason will feature the entire best-of-seven NBA Finals in primetime on ABC.

and

ABC, ESPN and ESPN2 will also televise up to 30 playoff games in the first two rounds, while ESPN will feature exclusive coverage of the conference semifinals games it televises and one of the conference finals each year.

Note that there is no accounting for additional "per-game" payments, so the two broadcast partners of the NBA are paying a flat fee every year for the entire package of games (both regular season and playoffs).