Your book is wrong, and the first sentence is fine. Except that there should be a determiner before the single count noun *bribe*.

What you are basically asking is: Can we use the present perfect in both the *"since"* clause and the independent clause in such a sentence as

>Since my father *has joined* this post, he *has not taken* (a) bribe. 

The answer is yes, and I will show this with many real world examples written by native English speakers.

Note that in less formal contexts, the present perfect is usually expressed in contracted form, so that your sentence would be either:

>Since my father's joined this post, he's not taken a bribe

or

>Since my father's joined this post, he hasn't taken a bribe.

Thus: *my father has joined* becomes *my father's joined*; and *he has joined* becomes *he's joined*; and *I have joined* becomes *I've joined*, etc. 

There is no grammatical reason why the present perfect cannot be used in both clauses, and your book and sources that say the same thing as your book are wrong.

Here are many examples from real world English. Note that in each example the  *"since"* clause is talking about duration over time and not as a synonym for *because*:

I found all these examples using this google Books search (["since he's joined"](https://www.google.com/search?tbm=bks&q=%22since+he%27sjoined%22+he+never+cals+anymore#tbm=bks&q=%22since+he%27s+joined%22)).  And I have even ignored the first one I get ("Ever *since he's joined* the Powhatan council as a sub chief *he's had* to put aside many of his opinions of them", because it uses the word *ever*, but really that makes little difference.)

>Why, *he's been* almost like a son to me *since he's joined* us — learning with me.

>*Since he's joined* the outfit, *he's opened his yap* about three times a day — usual at grub time, when if a man loosens up at all, he'll loosen up then.

(Note: the above perhaps uses "usual" in a dialectal way, but this does not invalidate the use of the clauses we are interested in.



>...he's unreliable and since he's joined up* with that damned American. *he's become* insolent into the bargain.

>*I've come* close to wringing Sajjad's neck many times *since he's joined* us.

Note the change in subject from *I* to *he* in the two clauses does not matter as far as the grammar of your question goes.

>*David has been* invaluable *since he's joined* our unit. 

>{Do you know that} *I've never even approached* him about his hitting *since he's joined* the team?

>Michael *has done nothing* but help us *since he's joined* us, and you can trust him ...

>*I've watched him* carefully *since he's joined* the chain, and the one thing he is not, is lazy. He has filled more plastic bags than Peter and me put together I point this out to him.

>Well, ESPN's "SportsCenter" anchor Stuart Scott (who coined the above phrase) *has been* on a roll ever *since he's joined* the network in 1993. 

Again, an *ever* in the above, but it can be deleted with little change in meaning. It serves as an intensifier. It doesn't change the grammar of the underlying statement.

>But I must say, *it's been* a week now *since he's joined* the queue for No. 24. 

Tired of *since he's joined*? How about some *since she's joined*?

>There's those who think *May's gotten* [May has gotten] real standoffish *since she's joined up* with the red hat ladies,” Velma said

>'When I say she hasn't had it easy, I'm not talking about the ragging *she's had* *since she's joined* the police,' Turner told him. 'I'm talking about before.'

>In the three weeks *since she's joined* AA, *she's already volunteered* to be in charge of refreshments and cleanup.

>Vashni *has proven* her usefulness time and again in the short time *since she's joined* us.

>*She's been* really innovative *since she's joined* us.

>the Ways and Means Committee *has never been* the same *since she's joined* with us.


>In the ten months *since she's joined* my family, *I've had* my hands full coping with her puppy hijinks,...

I do not have time, now, to add other examples, such as *since I've joined*, or even to search for verbs other than *to join*, but I hope these real world examples show that your first sentence agrees with the usage of native speakers, and that your book is wrong

Please note that it does not matter if this usage (using the present perfect in both clauses) is less frequent than some other usage; what matters is if it is "grammatically correct."  


You can also use *since he's joined* with a present tense in the independent clause:


>But, on the other hand, the only thing he's known *since he's joined* the Department is special treatment.

>*Since he's joined* the Night Guard, I swear he's spying on me.

>Always was; but, *since he's joined* the proletariats in America, he's stark, staring mad. 

>...*since he's joined* the church, he's worse than ever.