This has come up somewhere else a few months ago, and no one could give a definitive limit for the third rail - although it was generally agreed it never reached Terminus.
Vic Mitchell's book on that section of the SWML confirms that all three sides of the triangle had third rail as of 1969 (on plate 114) and I reckon if the idea was to use the triangle for turning electric trains you'd have to assume it went at least a couple of hundred yards south of the 'south to west' junction.
(I see that junction was known as Southampton Jn - you learn something new every day...

)