Jamieson, Fausset and Brown on Nehemiah 10:38

38. the priest the son of Aaron shall be with the Levites, when the Levites take tithes--This was a prudential arrangement. The presence of a dignified priest would ensure the peaceful delivery of the tithes; at least his superintendence and influence would tend to prevent the commission of any wrong in the transaction, by the people deceiving the Levites, or the Levites defrauding the priests.

the tithe of the tithes--The Levites, having received a tenth of all land produce, were required to give a tenth of this to the priests. The Levites were charged with the additional obligation to carry the tithes when received, and deposit them in the temple stores, for the use of the priests.