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Going by the letter of the 5th edition rulebook.
should the same multiplier for the  cash reward  for example  *3 be applied to the karma calculation?

Lets say you have  a  base 3000N per player *3 , this would give them  9000N as a reward.
if you calculate  they should earn 5 karma according to the table,  does this get multiplied *3 for  5*3= 15 Karma?

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No

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The multiplication of nuyen is determined by the highest dice pool the PCs will encounter. This isn't used for karma.

What karma uses that is also used by nuyen is a modifier. The effect of the modifier is different based on what it is your calculating. Nonetheless if a run is cold-hearted or feel-good, that same modifier is applied to both karma and nuyen.

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While you can't get paid for it being a "cold hearted run" and get karma for a "feel good run", and have to use the same for either, for nuyen it's a +/- 10-20% modifier, for karma it's just a static +/- 2 karma.

Dice pool is used in both as well.
While (Dice Pool/4) is a modifier for nuyen, (Dice Pool/6) (rounded down) is added as karma.

The difference is, nuyen it's generall multiplicative modifiers, while karma is strictly additive.
 
So again: No you don't after you added the karma together then multiply it by the nuyen multiplier. Different things.