Telling the imaam to wait

There is no basis for this; it was not done at the time of
the Sahaabah (may Allaah be pleased with them) and it is not something that
they taught. It also disturbs the others who are praying with the imaam, and
disturbing other worshippers is something that is not allowed, because it
distracts them. 

The Prophet (peace and blessings of Allaah be upon him)
went out one night to his companions when they were praying and raising
their voices in recitation. He told them not to do that and said: “Do not
raise your voices above one another when reciting Qur’aan.” (Maalik in
al-Muwatta’, al-Salaah, 29). According to another hadeeth: “Do
not disturb one another and do not raise your voices above one another when
reciting Qur’aan.” (Abu Dawood, al-Salaah, 1332). This indicates that
everything that disturbs the people who are praying behind the imaam is
forbidden, because it disturbs the worshippers and interferes with their
prayer.

 With regard to the imaam, the fuqaha’ (may Allaah have mercy
on them) said: if the imaam senses that someone has come in to join the
prayer, then he should wait for him, especially in the last rak’ah in which
the latecomer may catch up with the jamaa’ah, because the Prophet
(peace and blessings of Allaah be upon him) said: “Whoever catches up with a
rak’ah of the prayer has caught up with the prayer.” (al-Bukhaari,
al-Mawaaqeet, 580; Muslim, al-Masaajid, 607). But if it will
cause any hardship for the members of the congregation then he should not
wait, because they are more deserving of consideration than the one who has
just come in, because they were there before him.