Welcome to the forums.
Sorry that you found the power module manual a bit 'murky'.... We try really hard to make them clear.
If you have any input on how to make it clearer, lets know.
On page 1 of doc 1453, we show in the text under 'Description' the three types of power modules we offer and what CT's each requires.
Same again at the bottom right of page 1 in the table.
AIPM is single phase 1-10 amp input
AIPM-3 is three phase 0 to 5 amp input
AIPM-3V is three phase .333VAC CT input.
This is then broken out in the wiring diagrams for each of the modules.
Page 11 has the heading 'Wiring Diagrams - SNAP-AIPM'. If you are going to be measuring less than 10 amps current, you can skip the CT altogether as shown on the top left of the page.
If you need to measure more than 10 amps, then you can use a 5A CT as shown on the diagram at the bottom right of that page.
Page 14 is for the AIPM-3 and the diagrams mention using 5A CT's.
Page 16 is for the SNAP-AIPM-3V and shows using .333VAC CT's.
So, to answer your question, yes, you need a CT with a current secondary, not voltage, to measure current with the SNAP-AIPM module.