The answer
Both the NKJV and the online Septuagint version that you have cited follow the current Hebrew numbering. Whoever posted the online Septuagint simply chose to use the current Hebrew numbering instead of that of the Septuagint. Not only is this a mistake, but Psalm 151 is listed under the number 151, whereas in the Septuagint this psalm is printed after Psalm 150 with a preface stating that it is "outside the number". This shows that at some point the Fathers chose to restrict the Psalter to 150 psalms, after which the Greek-speaking Fathers added another psalm of King David but chose not to actually number it. Whoever posted the online version made another mistake, though, by adding the Prayer of Manassah as Psalm 152. This is not found in any LXX mss. These are minor mistakes, if one even chooses to call them that.The Agpeya follows the actual Septuagint numbering as you described. The current Hebrew and the Septuagint are the same up to Psalm 8. Psalm 9 in the Septuagint corresponds to Psalms 9 and 10 in the Hebrew. It cannot be proven whether the Hebrew currently separates an original one psalm or if the Septuagint combines two. The same can be said for the other two examples cited. Apostolic Christians, however, have always followed the Septuagint. The only psalms that match up in the two numbering systems are 1-8 and 148-150.
Answered by His Eminence Metropolitan Youssef (opens in a new tab)