Let's see who finishes/will finish first.

Hi,everyone. I saw a grammar book saying that in the following case we can use pressent/future tense in a relative clause:

Let's see who finishes/will finish first.

But that book doesn't explain clearly in what condition can this rule be applied to. I guess maybe it's because the imperatives. So I've found several similar cases to let everyone see if they could all use pressent/future tense in the relative clauses:

Let me know how you are from time to time. (Can we say "Let me know how you will be from time to time." ?)

Let's see who gets there first. (Can we say "Let's see who will get there first." ?)

Come back in a week and tell me what you think then. (Can I say "Come back in a week and tell me what you will think then."?)

Make sure you come back soon. (Can I say "Make sure you will come back soon." ?)

If it is not because imperatives, then why can the first sentence use pressent/future tense in its relative clause? Please enlighten me with this, thank you!