"once put" vs. "once it is put"

Solution 1:

"Once" is a subordinating conjunction here in the sense "when" or " as soon as". Like any other adverbial conjunction "once" can also locate the action of the main clause in the time frame being subservient but lending meaning to the main clause. ' Once ' may precede an adverbial clause or phrase.

Without "it is" the first part of the sentence is a reduced adverbial clause, a phrase. All 0/-ed/-en forms with out tense conjugation are passively adjectival. You're at liberty to use the reduced clause or its unabridged form. It's a matter of preference, nothing more to it.

Solution 2:

Once can also be used as a synonym of when. In addition to that, you can also use "on" or "upon" if you want to use fewer words in your sentence. So, instead of saying;

When the box was opened, it caught fire.

You can say;

Upon being opened, the box caught fire.