JOEL - According to our Doctrine and Covenants:

"Behold, now it is called today until the coming of the Son of Man, and verily it is a day of sacrifice, and a day for the tithing of my people; for he that is tithed shall not be burned at his coming.
For after today cometh the burning—this is speaking after the manner of the Lord—for verily I say, tomorrow all the proud and they that do wickedly shall be as stubble; and I will burn them up, for I am the Lord of Hosts; and I will not spare any that remain in Babylon." (D&C 64 23-24)

According to the scriptures, it is the wicked and proud who will burn. There are many good and righteous people who are not members of the LDS Church who will not be burned at Christ's second coming. Just because they have not made the same promises to live certain gospel principles that LDS have made(including paying tithing), does not mean that they are proud and wicked. Notice that God says that it is "a day for the tithing of MY people", meaning it is those who belong to His kingdom on earth who are obligated to pay tithing.
God knows the hearts of those who do not yet belong to His earthly kingdom and knows that when given a fair chance they would embrace His true gospel, including those who don't yet believe in Christ.
Our scriptures also say:

"All who have died without a knowledge of this gospel, who would have received it if they had been permitted to tarry, shall be heirs of the celestial kingdom of God;
Also all that shall die henceforth without a knowledge of it, who would have received it with all their hearts, shall be heirs of that kingdom;
For I, the Lord, will judge all men according to their works, according to the desire of their hearts." (D&C 137:7-9)

Because God knows the hearts of all good people, they will be spared from the burning that will consume the truly wicked. On the other hand, LDS people who have been baptized and endowed in the temples, have made solomn promises to God to obey His commandments(includinig the payment of tithes). If they break this contract through their proud and wicked actions they are more in jeopardy of burning at Christ's coming than the non-Christian who has not made those promises.
The payment of tithing alone is not the only thing that is going to keep a person from burning. There are of course a lot of other things that a person must do or not do to keep himself righteous before God. I think also a point that God is making about tithing is that a person who is willing to sacrifice worldly goods is likely to not be the type of proud or wicked person that would qualify for destruction.