How are t-butyl substituents named according to IUPAC nomenclature?
According to Nomenclature of Organic Chemistry: IUPAC Recommendations and Preferred Names 2013 (Blue Book) (P-57.1.2), the preferred prefix for $\ce{-C(CH3)3}$ is "tert-butyl".

As for where it comes in the name:


  P-14.5 Alphanumerical order
  [...] Alphanumerical order is applied as follows in organic nomenclature. Nonitalic Roman letters are considered first, unless used as locants or part of a compound or composite locant [...]


so the prefix tert is not considered (except in more complicated cases, cf. P-14.5.3). Therefore, the preferred IUPAC name for the molecule in question is 1-tert-butyl-5-heptyl-2-propylcyclononane. Note that there are no parentheses around tert-butyl.

Be warned: tert-butyl has received special treatment from IUPAC on this front. Other non-systematic prefixes have fallen from favour, most notably isopropyl, sec-butyl, and isobutyl. The preferred prefixes are respectively propan-2-yl, butan-2-yl, and 2-methylpropyl.