I heard the following on a TV serial:
Yes, of course. That's exactly what a good publicist should say, isn't it?
I can see the tag question 'isn't it' is tagging 'That is exactly ...., isn't it?'.
Instead of 'isn't it' is it also acceptable to tag it with 'shouldn't s/he?, because the statement is 'That's exactly what a good publicist should say'
By the way, I had read somewhere and also observed that in Indian English, the common tag question is 'isn't it' whether it is quite correct or not. For example, 'He sold it, isn't it?', or 'He didn't come, isn't it?' I remember there was a section about something like this in the entry for 'Indian English' on Wikipedia, but I can't seem to find it there anymore. Well, somebody must have removed it, isn't it?