The sentence I will tell him (that) I will go to the cinema is an example of reported speech. I will go to the cinema is a reported clause.
The main verb in reported clauses can be in any tense. For example:
- I will tell him I went to the cinema. (past)
- I will tell him I plan to go the cinema. (present)
In this case, the cinema visit is in the future, so a future construction is used:
I will tell him I will go the cinema. (future with will)
The second sentence contains a temporal clause, namely before I arrive. As Swan states in Practical English Usage (p99) in the section called present tense with future meaning:
With before, we use a present tense if the meaning is future.
- I'll telephone you before I come. (not ...
before I will come.)