We use the first conditional to talk about something that will happen (the result), if a particular condition (which is likely to happen) is met. Because the manager is asking Tim to work in the stockroom, it’s likely that Tim will do it and that’s why we use the first conditional here.

In order to get an interview, Tim has to work in the stockroom.
If you do this for me, you’ll have a chance of promotion.
If Tim works in the stock room, he will get an interview.
If Tim doesn’t work in the stock room, he won’t get an interview.

So, the meaning is that if the condition is met (and it’s more than 50% likely to happen) then the result will happen.

When we use will in the result clause of the first conditional, we are certain that something will happen. It is definite. But we can use may or might instead of will. This means that the consequence is not certain. It is possible, but not definite.

I'm not feeling very well. If it rains tomorrow, I’ll stay at home.
I'm feeling fine and I've got a car. If it rains tomorrow, I might stay at home, or I may go shopping. I'll decide tomorrow.

Note: In the first conditional, there is no difference in meaning between may and might.

In conditional sentences, you don't always use 'if' or 'if not'. You can use 'provided that' or 'so long as' instead of 'if'.

For example:
If you put down the gun, I won’t call the police. =
So long as you put down the gun, I won’t call the police. =
Provided thatyou put down the gun I won’t call the police. =
(Provided that is more formal than if. )

You can use 'unless' instead of 'if not'.
For example:
If you don't put the gun down, I'll call the police. =
Unless you put the gun down, I'll call the police.