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 there should be a determiner such as *a* or *one* before the single count noun *bribe*.

First, a reminder of what the present perfect does and why one might want to use it in a sentence such as yours.

Using the present perfect makes the past action of *to join* relevant to the moment of speaking. It refers to the whole duration or length of time between when the father first joined the club and right now, when the sentence is said. A rough paraphrase is 

>*Since my father first joined the club all the way up till right now*, he has not taken a bribe. 

If  you were defending your father against someone who has  accused him of taking a bribe, you might want to use  the present perfect tense because of how it connects the past action with the present moment. 

Now, a dozen examples from real English, not textbook English. 

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. 

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 no difference as to whether the sentence is grammatical.)

Examples:  

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

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

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

>*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.

Note that *he's unreliable* is a contraction of *he is unreliable* while *he's joined up* is a contraction of *he has joined up*. Every use of *he's  joined* in these examples is  a contraction of *He has joined*. 

>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 without changing  the grammar of the underlying statement.


>*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.

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



>*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.



>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*, *since you've joined*, *since we've joined* and *since they've joined*; to search for uncontracted versions of any of the above; or to search for any verbs other than *to join*; but I hope these real world examples show that your first sentence agrees with the usage of native speakers. 

You can also turn any of these examples into a question. For example:

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

and

>*Has Michael done anything* but help us *since he's joined* us?

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."  So, in sum, I have no idea why your book says that the second sentence is the correct one of the two. 
<hr>

You can also use *since he's joined* with the simple 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.