Given t-undercurl-pink.vim:

let &term = 'tmux-256color'
hi SpellBad cterm=undercurl
set spell

" misspellet

vim -Nu t-undercurl-pink.vim t-undercurl-pink.vim will cause a pink cursor color for me (with rxvt-unicode as the terminal), and keeps it on exit. It does not happen when using gnome-terminal.

This appears to be related to t_Cs being set incorrectly:

% TERM=tmux-256color vim --cmd 'echom &t_Cs' -c q
^[]12;%p1%s^G

Via #2424 (comment).
I've just tried #2126, but it does not appear to fix it.