Question: In Plants vs Zombies, are there strategies that make it more probable to have certain plants (for your Zen Garden)?

How does the game decide which plant is given?

Answer: 
I believe the game hints mention that certain types of plants only appear in certain types of boards or levels.

For aquatic plants, you need to be playing an aquatic level.

For plants for your fungus garden, you need to be playing a night level.
According to the tips given by the Zen tree, yes playing certain areas increases your chances of getting certain plants. Play the pool levels to get the plants for the Zen garden aquarium plants. It increases your chances but is no guarantee you will still get the other Zen garden plants too.