There is a difference between "collecting" the cactus and "destroying" the cactus. The cactus needs to make it to the bottom of the board and into an exit lane to be “collected.” When you collect a cactus, you will see the flowers bloom before it collects. (Exit lanes are marked with a whitish triangle at the bottom, like an arrow pointing downward.) When your level requires a certain number of cacti, it is asking you to collect them. But destroying cacti is also very useful, particularly for hard-to-reach top corners.
If you directly drop the cactus 2 or more tiles or if you hit it with a power tile, it will burst. The only exception to this is when it drops directly into its exit spot (the bottom of the lane with a grey arrow beneath). In this case, it will bloom and collect instead of bursting.