How does the thunderstorm from Plant-fed Lightning Reeds choose targets

Here is a table from Plant Food:

Peashooter: Turns them into faster-shooting Gatling Peas for three seconds. They shoot approximately 20 peas a second.
Sunflower: Produces 150 sun.
Wall-nut: Gives it a hard armor shell for extra strength.
Potato Mine: Arms itself and produces two armed Potato Mines on other spaces.
Cabbage-pult: Launches several cabbages at once, hitting every zombie and grave onscreen.
Bloomerang: Shoots approximately ten boomerangs in four directions, up, down, left and right.
Iceberg Lettuce: Freezes every zombie on screen, similar to the Ice-shroom.
Twin Sunflower: Gives 250 sun.
Bonk Choy: Punches zombies in every direction at a very fast rate.
Repeater: Shoots like a Gatling Pea at first, but at the end it shoots a 2x bigger Pea.
Kernel-pult: Launches several butter at once, hitting every zombie and grave onscreen.
Snapdragon: Sets a 3x3 area in front of it on fire killing all zombies on those spaces.
Spikeweed: Temporarily fills the row with other spikes poking up from the ground and pulls zombie to the Spikeweed.
Coconut Cannon: Fires one big Coconut that kills all zombies in a row.
Spring Bean: Bounces all zombies on screen.
Spikerock: Temporarily fills the row with other spikes poking up from the ground and pulls zombies to the Spikerock.
Threepeater: Shoots a wildfire of peas across the area.
Split Pea: Both heads shoot peas like fast-shooting Gatling Peas. The Repeater head fires a big pea at the end.
Chili Bean: Launches 3 extra beans randomly.
Lightning Reed: Makes a storm cloud that damages the zombies with lightning.
Tall-nut: Gives it a hard armor for extra strength like Wall-nut.
Pea Pod: Gains a giant Peashooter head that shoots five big peas which do a lot of damage.
Melon-pult: Launches melons out from the top that does 2x the damage to all zombies.
Winter Melon: Same as Melon-pult with added slowing effect.
Imitater: As the Imitated Plant
Snow Pea: It shoots a lot of frozen peas
Torchwood: The fire becomes napalm.

For full information there is the website above.

So I just went through the start of the game on a new profile, and indeed you should have pea shooters:

(Ignore the extra plants, they rolled over from my main profile)

The first thing I'd recommend is to delete and recreate your profile on the home screen. If you opted to skip the tutorial the first time, try going through it. If you went through it the first time, try skipping it.

If after deleting and recreating your profile you still don't have the pea shooter, complete day 2 which will unlock the cabbage-pult, which is nearly identical to the peashooter in terms of cost and damage output. As you progress, you'll unlock plants that are vastly superior to the pea shooter anyway.