It doesn't follow the usual paradigm, but that doesn't make it incorrect. This is a literary device to describe the action more vividly. Note also the use of "there came out of it a hungry tiger", rather more literary than the usual "a hungry tiger would come out of it". This is definitely not a sentence you would normally hear in an everyday conversation! So the author is not likely to want to tell the story using everyday language, right?

CJ

- (The choice was his alone.) If he [opened] the door, there [came] out of it a hungry tiger which immediately jumped on him and tore him to pieces as punishment for his guilt.

This is from a book. Is this sentence correct?

JT: PERFECTLY CORRECT; just a bit literary and reminiscent of an older form of English [possibly even an older subjunctive form; why isn't anyone complaining about this one?].

Should it be "If he opened the door, there would come out ... "?

JT: Your sentence sounds a bit funny, Jandi; the "there would come out". POSSIBILTY, it too is an older style subjunctive form.

But now we have a situation that illustrates how and why ENLs choose these expressions using present tense or past tense FORMS. [historical past tense forms in the case of modals]

Put yourself in that person's shoes, Jandi. Again, the choice is entirely yours.

Jandi: If I open the door, a tiger will come out and devour me.

Jandi If I opened the door, a tiger would come out and devour me.

Both are certainly possible. Choosing illustrates that the speaker doesn't want to do that; the speaker puts it more into the realm of the highly improbable, a position that the speaker wants it to be, for obvious reasons.

If I opened [for this situation] is saying, "Not that I would but if did, then this would happen".

"If I open the door, a tiger will ..." is allowing that it is a more real chance.

Even a mixed conditional is possible,

"If I open the door, a tiger would ..."