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
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.
The past action of the "since" clause is to join. 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 person might want to use the present perfect to stress the fact thatrough paraphrase is
For instance, ifIf you were defending your father against someone who accusedhas 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.
More examplesExamples:
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 ...
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.
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 ...
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.
But I must say, it's been a week now since he's joined the queue for No. 24.
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, 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." So, in sum, I have no idea why your book says that the second sentence is the correct one of the two.