I have one in my car as well. When I connect my Note3 android phone and play music or a podcast, I have to max the volume on my phone and I still usually run the radio volume a little higher than I would if I had a CD or just plain radio (18-20ish versus 12-14 normally). Not so bad it distorts but enough that I have to remember to turn it down when I switch back. I had to do the same (max the volume) in wife's Highlander with a factory bluetooth setup so I'm assuming this is normal.
The way the Jazzymod works is it intercepts the signal between the cd changer and the radio itself. Apparently the stock radio doesn't stop "listening" to that wire when you switch to the fm radio input, it just powers down the CD changer and assumes there won't be a signal. That's why you can hear it as long as the radio is powered on and your pushing something in via the jazzymod.