In 'Alenu Leshabbeyah, when we come to the phrase, "WeAnahnu Mishtahawim Lifneh Melekh Malkhe Hammelakhim Haqqadosh Barukh Hu", which means, "And we bow before the King of kings, the Holy One Blessed be He", we must actually, physically bow as we recite those words.
Even though we only bow while actually recite that verse, nevertheless, if somebody who has already prayed walks into the Synagogue at the moment when they are saying that phrase in 'Alenu Leshabbeyah and bowing, he must also stand and bow with them.
This is because we do not want someone else who might be watching them to think, that the reason why he is not bowing is because, G-d forbid, he is denying what we state in 'Alenu Leshabbeyah.
(See 'Od Yoseph Hai, Ki Tissa, Othe Kaf Beh)
