Yes, precisely. Transjordan was separately administered beginning in 1924. The language in the paragraph gives the mistaken impression that Transjordan was always referred to as such even prior to being split off from Mandatory Palestine in 1924.  

 I think that unless there is evidence for references to Transjordan prior to 1924, the language that I cited should be removed as misleading and unecessary. There is no need to say that the area east of the Jordan was referred to as Transjordan if it was only referred to as Transjordan after Transjordan was created. 

 In any case, the use of the word "considered" unecessarily weakens what is an undisputed historic fact, which is that the original Palestine Mandate was on both sides of the Jordan River.