As Kate pointed out, in your particular example "when" would be better than "after". But since you're curious about "after", let's talk a little more about it. The choice of tense depends on the context.
Here are some examples with the present simple tense:
I'll come to your place after I pick up the kids from school.
We'll probably get some dinner after we watch the game.
Both sentences have the basic structure of "A will happen after B", and the B is not what's interesting - rather, the emphasis is on A (coming to your place, getting dinner). Compare this with the following examples using the present perfect:
I'll go there after I have finished my meal.
Our guests will join us after they have checked in to their hotel.
The structure here is again "A will happen after B", but now we're putting a little more emphasis on the B (finishing the meal, checking in) by indicating it's going to take some time, so A will have to wait until B is done.
This isn't meant to describe a formal grammatical rule - I'm just trying to give you a taste for the difference.