That's roughly right. RAI is AFNI's default coordinate order. You can change this with the AFNI_ORIENT environment variable if you like. What RAI means is with coordinates given as (x,y,z), x increases from Right to left, y increases from Anterior to posterior, z increases from Inferior to superior. For most standard spaces, this amounts to left and right being symmetrically around zero with right negative and left positive. To make this a little more confusing, this exact same order may be called LPI in other software packages if the packages determine order by the most positive dimension. The coordinates are presented in AFNI with left, right, anterior, posterior, inferior, superior shown in the coordinate/crosshair panel in the upper left part of the afni GUI.

Many published papers use LPI, and we provide the LPI order in our whereami reports. MNI and Talaiarach are "spaces", not coordinate orders, so locations within either can be expressed in any of the 27 potential variants of coordinate order, but RAI and LPI are typically the most commonly used. I hadn't looked at the Analyze order, but I found a document that shows what appears to me to be RAI, in our terminology.