"After I read well, Dad gave me a sweet."
Translation:Après que j'ai bien lu, Papa m'a donné un bonbon.
bien is acting as an adverb and the position of adverbs in a compound tense is as follows:
In French an adverb usually follows the conjugated verb. Thus, in all compound tenses adverbs are placed right after the auxiliary and just before the past participle. A compound tense is where an auxiliary is required, such as the passé composé The passé composé is made up of a conjugated form of the auxiliary être or avoir + the past participle of the verb.
Nous avons bien mangé - We ate well
Tu as bien travaillé. - You worked well.
Elle est vite partie. - She left quickly.
Ils ont beaucoup aimé le film. - They liked the movie a lot.
Quelqu’un a mal fermé la porte. - Someone closed the door badly.
Tu as beaucoup changé. - You have changed a lot.
J'ai déjà entendu cette chanson. - I have already heard that song
elle a toujours su - She has always known
If the conjugated verb is in the negative, the adverb follows the negation.
j'ai trop mangé. Je ne vais pas bien dormir. - I ate too much. I am not going to sleep well.
tu n'as pas beaucoup mangé! Juste de la soupe! - you didn't eat too much. Just some soup
Il ne me trouvait pas généralement. - He usually did not find me.
here is an explanation of when to use après que and après
après + noun / pronoun without an associated conjugated verb
après + verb in the past infinitive (past infinitive indicates an action that occurred before the action of the main verb, but only when the subject of both verbs is the same)
après que + a clause with a conjugated verb
Il part après son repas - He leaves after his meal
Il part après qu'elle a mangé - he leaves after she has eaten
Il part après avoir mangé. - He leaves after eating
C’est bon de boire une bière après le ski. - It is good to drink a beer after skiing
Après avoir marché pendant une heure, j'étais perdu - After walking for an hour I was lost
Je dois commencer après qu'il part. - I must start after he leaves.
Je dois commencer après son départ - I must start after his departure. Deux ans après que je suis parti - Two years after I left
Après cela il a marché - After that it worked
Après que je l'ai frappé, il a marché - After I hit it, it worked
Je pensais qu'ils en avaient après toi - I thought they were after you
I think this one makes sense. I missed it because I left out "que" but it is logical that it should be there since there are two clauses and they need a conjunction to be connected. It is the same in English, except that we allow the word after to act as conjunction. In fact, the conjunction is the third of seven definitions of "after" in Mirriam-Webster's on-line resource.
See also nicholas_ashley's comments above.