Doesn't cycle through popup completion menu when started by neocomplete

[gotgenes]

My example VIMRC

set nocompatible

set runtimepath+=~/.vim/plugins/repos/github.com/Shougo/dein.vim

" Required:
call dein#begin('~/.vim/plugins')

" Let dein manage dein
call dein#add('Shougo/dein.vim')
call dein#add('Shougo/neocomplete.vim')
call dein#add('SirVer/ultisnips')
call dein#add('honza/vim-snippets')
call dein#add('neitanod/vim-clevertab')
call dein#end()

filetype plugin indent on
syntax enable

if dein#check_install()
  call dein#install()
endif

let g:neocomplete#enable_at_startup = 1

call CleverTab#NeoCompleteFirst()

Steps to reproduce the behavior

1. Start Vim using the VIMRC above and edit a file; best to just use the VIMRC as the file
2. Invoke :call CleverTab#NeoCompleteFirst() (See discussion in #1.)
3. Induce neocomplete to bring up the popup menu by typing 3 characters; for example neo
4. Try to use <Tab> to select the completion
5. Observe that no action takes place