Praise be to Allah.
The one who is praying behind an imam should do what he thinks is Sunnah, whether the imam does it or not, unless what the individual does will lead to problems in following the imam, such as doing something too late after him or doing it before him. In that case, he should refrain from doing what he thinks is Sunnah, for the sake of following the imam properly.
What the questioner asked about – raising the hands before and after bowing – will not lead to any problems in following the imam, so he should still do it.
An example of something that will lead to problems in following the imam is if the one who is praying behind him thinks that it is mustahabb to sit and rest briefly (after the second prostration, in the first or third rak‘ah, when it is not followed by tashahhud) and the imam does not. In that case the one who is praying behind the imam should refrain from doing it.
This has been explained in the answer to question no. 34458
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
With regard to matters that will not lead to doing something too late after the imam or doing it before him, the one who is praying behind the imam may do what he believes is correct. For example, if the imam does not think that the hands should be raised when saying the takbeer before bowing, when rising from bowing and when standing up after the first tashahhud, but the one who is praying behind him thinks that this is mustahabb, then he may do that, because it will not lead to him doing something too late after the imam or doing it before him. Hence the Messenger (blessings and peace of Allah be upon him) said: “When he says takbeer, then say takbeer, when he bows, then bow, and when he prostrates, then prostrate.” The fa (translated here as “then”) indicates that one thing is done immediately after the other. Similarly, if the imam sits mutawarrikan ( i.e., sitting with the left foot forward and holding the other foot upright, sitting on one’s behind) in every tashahhud that is followed by the salaam, even in the two rak‘ah prayers and the one who is praying behind him does not think that he should sit mutawarrikan except in a second tashahhud of prayer in which two tashahhuds are prescribed, then in this case he may refrain from sitting mutawarrikan with his imam in a two-rak‘ah prayer, because this will not lead to him doing something too late after the imam or doing it before him. End quote.
Ash-Sharh al-Mumti‘, 2/319-320
And Allah knows best.