Probuđivati se doesn't exist.
You should say : buditi se - to wake up (it is used for action that repeats every day)
Just like in your first example: I wake up at 6 every morning - Budim se u 6 svako jutro.
probuditi - to wake up (for the action that is finished)
The second example is past tense for the action that is finished (simple past tense in English. You get it like this:
Personal pronoun (ja, ti, on, ona, ono, mi , vi, Vi, oni, one, ona)
+
verb to be (in the present tense): sam,si,je,smo,ste,su
+
at the end of your word, you put: o - m /la - f /lo - n /li - pl. / le - pl.f. /la - pl.n.
In your case, that would be: Ja sam se probudio
I hope this helps. If you have any questions more, feel free to ask me. I'll be so glad to help you.