Found the solution:
Updated my .vimrc to:
if exists('$TMUX')
let &t_SI = "\<Esc>[3 q"
let &t_EI = "\<Esc>[0 q"
" these two lines were outside the if statement
" putting them here solves this issue although the cursor shape stays
" the same in any mode outside tmux - but that's OK.
let &t_SI = "\<Esc>Ptmux;\<Esc>\<Esc>]50;CursorShape=1\x7\<Esc>\\"
let &t_EI = "\<Esc>Ptmux;\<Esc>\<Esc>]50;CursorShape=0\x7\<Esc>\\"
endif
Thank you for pointing me towards this.