On the website: "Hebrew Nations" the 'two-tithes' proposition is outlined:
The Two Tithes
The Tribe of Levi was divided into 2 major sections, Cohens (Priests) and Levites. The First Tithe was divided between Cohens and Levites. The Cohens had to receive a first portion of the grain, wine, and olive oil harvests. These comprised the staple foods at the time. "The first of your grain, wine and oil... you shall give him" (Deuteronomy 18:4). A tithe (a tenth) of the remainder was to be given to the Levites, as it says "And to the children of Levi I have given all tithes in Israel... (Numbers 18:21,24).
A Second Tithe of the remainder is to be set aside. In the 1st, 2nd, 4th, and 5th years of the Sabbatical Cycle it is to be eaten in Jerusalem (or to be redeemed and the proceeds spent for food to be eaten in Jerusalem), as it says "You shall tithe all the produce of your crops... and shall eat before Ha-Shem your G-d in the place that he shall choose" (Leviticus 27:30-31, Deuteronomy 14:22-23). In other (3rd and 6th) years this tithe is given to the poor and Levites (Deuteronomy 14:28-29, 26:12).".
The "two-tithes" view is also explained in the Wikipedia article: "Poor tithe",
The early rabbis, the Tannaim and Amoraim, understood these texts as describing two separate tithes: the first tithe to be given to the Levites and the second tithe, in Leviticus 27:30, to be kept by its owner and to be eaten in Jerusalem, except in the third and sixth years of the sabbatical cycle, when instead of separating the second tithe, the poor tithe was separated and given to the poor. The medieval commentator Rashi also interprets Deuteronomy 26:12 as referring to the third year, when the first tithe was given to the Levite and the poor tithe was given to "the stranger, the orphan, and the widow".
The 'one-tithe' view, on the other hand, is outlined in the article: "The Levites Place in Society", ("The Tithing Dilemma", chapter 8):
"Many people have not realized that Moses gave the Levites the means by which to earn a living without having a dependence upon tithe alone. Other than the tithe of the third and sixth years of a sabbatical cycle, the only Levites that received tithe were those who attended the service of the Tabernacle".
"A part of their tithe even went to support a type of social security service every third and sixth year for the destitute".
Which of the two views is the correct one? And, please, also explain why that is so.