Grammar-wise both sentences are fine. However, the first one with
... weil man nach einer Sternschnuppe immer einen Wunsch frei hat
is the more natural way of speaking.
I suppose the reason is as follows:
The "immer" works like a sign-post like: "Attention! Now something crucial is going to be said!", and thus it lets the audience focus on the element directly following.
In the first (more natural) sentence, this is "einen Wunsch frei haben". Which is indeed the specific thing - the core of the proposition.
... weil man immer nach einer Sternschnuppe einen Wunsch frei hat.
the element following directly on "immer" is "Sternschnuppe", so focus is laid on "Sternschnuppe". This may be appropriate in certain situations, but not in your case, as you had mentioned that Sternschnuppe already, so it is anyway present in the mind of your audience, and now everybody is just waiting what exactly you are going to tell about Sternschnuppen.
A sentence with "immer nach einer Sternschnuppe" would need something to be said where focus on Sternschnuppe makes sense. For example:
Ich mag Sternschnuppen lieber als Meteoriten, weil man immer bei einer Sternschnuppe einen Wunsch frei hat, aber bei einem Meteoriten nicht.
Disclaimer: in my experience wishing things on the sight of a Sternschnuppe has no effect. None of the wishes I spent on them became true so far.
(Okay, perhaps it is just because each Sternschnuppe is only for one wish, and every time somebody else is quicker. Perhaps there are too many people on earth, and too little Sternschnuppen around.)