obojętnie czy 'when' czy 'that'?

The moment that...
The moment when...
Obie te konstrukcje zawsze można używać naprzemiennie? Znaczą to samo?

Np.
"The moment when/that you do it, you make me smile.."
(W chwili gdy to robisz, wywołujesz mój uśmiech)

Just a quick supplementary note: "The moment you do it, you make me smile" is better than "The moment that you do it, you make me smile." Omit that here. It’s one of those situations where the relative that is not needed and less is more.

The moment you did it, all hell broke loose.
The moment he opened the valve, the oil gushed out from the tank.

Not needed? It's straight-up wrong. The "very" in "you're very welcome" is not needed. You are welcome, by the way.

Now, I have homework for you. Do we say The time Janski gives a 100% accurate reply, all hell breaks loose or The time Janski gives a 100% accurate reply, all hell will break loose.

In other words, do we insert the will there or is it, how shall I put it, "not needed"?