What is the logical way to understand Iso, Sec, Tert and Neo prefixes?
The prefixes, iso-, sec-, tert-, neo- are all traditional names when structural organic chemistry was still developing. You have already rationalized all except neo-. Neo- is Greek term for new. I looked up the OED etymological dictionary for older meanings, and the earliest use is traced to 1876. Now you can see in no 2, that neo- was a good option.


Used in the names of chemical compounds, minerals, etc., which are closely related to, or new forms of, known substances.
neocatechu  n. (Obsolete) a kind of catechu.
Used in the names of compounds and radicals in which one carbon atom is linked to four others.
Not part of standard chemical nomenclature although well established in neohexane and neopentane (and related terms).
(a)
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† neo-acid  n. Obsolete
1876   W. Odling in London, Edinb., &amp; Dublin Philos. Mag. 5th Ser. 1 216   The names which call to mind that the normal, iso-, and neo-acids are mono-, di-, and trimethyl &amp; etc. derivatives would seem to be most advantageous.



Neo- even it is used today represents a terminal tert-butyl group, just like the prefix iso- represents a iso-propyl group at the end.

IUPAC names have superseded all.