The 61 year old witness for the prosecution of the Floyd case broke down and cried uncontrollably.
Does the judge give instructions to the jurors that they cannot allow the emotions of the witnesses to influence their decision?
No. Jurors generally do not receive such an instruction and it is not a rule of law or evidence. Jurors have to rule in accordance with the law, but how they judge the credibility of witnesses may be influenced by emotional factors. How the witness says something is as much a part of the evidence as what they say.
The military has a saying “never give an order you know won’t be obeyed”. While the judge can tell the jury to disregard some statement or other, what that really means is that judge is saying that it is not relevant to the case for legal reasons.
But jury discussions are private, and what and why jurors make their decision are outside of the control anyone except themselves, except in the case of bribery, extortion, outside contact and similar outside influences. It would be totally impossible to (a) have a jury with real authority and (b) say that some of the jurors were ok because they voted one way after seeing/hearing something and other jurors were not because after seeing/hearing the same thing they voted differently.
Which is why mistrials exist, if there is something that they shouldn’t have to have seen, you hold a new trial and make sure they don’t see it.
But you can’t expect witnesses to be robots either, so you can’t shield jurors from emotions.
As a side note, whatever emotion you saw apparently didn’t sway you the way you appear to think it will sway the jury. Possibly it swayed you in the opposite direction. That’s the problem with juries, they make up their own minds.