That is correct. The SCHSSCA recommended a Soccer Penalty Chart to the HSL that was adopted in July 2001. It divides cards into 3 categories:

Category A (Fighting, attempting to strike; Foul, vulgar, abusive language or gestures; spitting at others)
Category B (Any straight red not mentioned above)
Category C Technical Red (Two yellow cards)

The punishments are as follows:

1st offense:
A - Next two games
B - Next game
C - Warning

2nd offense:
A - Player inelgible
B - Next two games
C - Next game

3rd offense:
B - Player inelgible
C - Two games

4th offense:
C - Player inelgible

The league rules on what the official writes up the red card as. In this case, the 1st was a Cat. C and the 2nd was written as a Cat. B.