It is likely that the newly installed amp is creating a ground loop, or it is picking up noise from the power source, and that is the source of your hiss.
Use a 'ground loop isolator' at the point where the signal goes into the new amp:
http://www.crutchfield.com/p_127SNI1/PAC-SNI-1.html?tp=2653
Also try a noise filter on the +12v running into the new amp.
http://www.crutchfield.com/p_003S25A/American-International-S-25A.html?tp=2653
This should be a relatively cheap and easy fix. Both filters can be had from crutchfield for ~$30, or from your local Radio Shack. You can install the noise filters yourself where the power and signal go into the new amplifier.
As your installer suggests, you might also want to turn down the gain settings on the new amplifier (usually little potentiometers that you turn with a small flathead screwdriver) to minimize the hiss. Just make sure that after adjusting the gain on the amp you can still adjust the volume to comfortable levels using the knob on the dashboard. You should be using about 75% of the range of the knob on the dash to achieve loud listening levels. i.e.- if you have the knob on the dash unit set to 10% and the music is already too loud, then turn down the gain on the amp.
Ask your installer to make sure that the new amp is hooked up correctly: i.e.- if you are running the speaker-level signal from the stock jbl amp into the new Memphis amp, then you better make sure that the new amp is set-up to handle speaker level inputs, or else you will fry the input stage on the new amp. The facts that you have made it this far and that it sounds good suggest that you are on the right track.
The problem with "bypassing the stock amp" as N8maher suggested is that I think Toyota uses a proprietary signal from the stock head unit to the stock amp on the 2003+ models. If you run the signal directly from the stock head unit to an aftermarket amp, I don't think it's gonna work. I have also heard that the nav system quits working if you remove the stock amp. It is all integrated.
So I would suggest keeping the stock amp in place. If you are running the signal out of the stock amp and into an aftermarket amp, just make sure the aftermarket amp is setup correctly to accept speaker-level inputs. Otherwise you could fry the input section of the new amp. Install ground loop isolator and line noise filter, adjust the gain on the amp and you'll be good to go.
Hope this helps.