It's probably because your starter is being given without being registered as "seen". All the usual methods of giving a pokémon to the player should add it to the seen list by default, but maybe you accidentally set that parameter to "false" or something. Does what you used look something like this?
Code:
pbAddPokemon(:PIKACHU,20,false)
If it does, change it to
Code:
pbAddPokemon(:PIKACHU,20,true)
or just delete the "false" and the last comma entirely (since it's set to "true" by default).
If that doesn't help, show us the code you're using to give the player this starter. I'm sure someone will know how to fix it, or, failing that, you can just explicitly set the starter species to "seen" by following
these instructions. Try making sure there's no "false" there first, though.
EDIT: On a second read of your problem, I'm wondering whether that's actually the case—if it's not already "seen", I'm not sure it would show up in the pokédex after you caught something. Maybe it might; my project doesn't really involve the pokédex or giving people normal starters so I've not really had a reason to play with that sort of thing, haha. Definitely give this a try first, though, and if it doesn't solve things then share any other information you have about your setup (which version of Essentials you're using, any addons, have you changed anything else, etc.).