"The one from Kcott "almost" worked. The double-quote fields are correct, the ones before the quotes are missing :)."
Yes, I forgot to capture the first part of the strings.
Fixing that, and then making changes for your altered input and updated spec:
$ perl -pE 's/^([^"]+")([^"]+)/$1 . $2 =~ y{\t}{,}r/e'
a b "x1 x2"
a b "x1,x2"
c d "x2"
c d "x2"
e f "x3 x4 x5"
e f "x3,x4,x5"
"I was not able to add "tabs" in the example ..."
Surely you must mean something else.
I pressed the key labelled "TAB" on my keyboard to add them to my input.
Admittedly, it may not be easy to see the difference between a tab and a space, but the output gives it away:
$ perl -pE 's/^([^"]+")([^"]+)/$1 . $2 =~ y{\t}{,}r/e'
a b "x1 x2"
a b "x1 x2"