Text me when you're there Vs. Text me when you'll be there.

In the context of that I'm talking to my friend who is going to a shop and I want him to call me immediately when he's there (and then for example I'll tell him what to buy there).

I have two choices:

Text me when you're there.

As far as I understand this choice more focus on texting when he's there, no matter when, but most of all is to texting when he's there, in the beginning or ending of his shopping.

Text me when you'll be there.

As far as I understand, this choice more focus on texting right when he's arriving there, not later.

I am not sure about my understanding and I'd like to know what's correct for my need (see the context in the beginning of the post).

The first is correct. You don't use 'will' after conjunctions referring to future time (e.g if, when, before, until, as soon as). In fact you might prefer 'as soon as' in your example. Text me as soon as you get there. Hope that's helpul.