It should be the OTHER way around! Tile roofs are much harder to clean then shingle roof are, and can easily use 2 to 4 times the amount of roof cleaning chemical.
Like Larry said, shingle roofs are always a 'walk in the park' compared to cleaning barrel or flat tiles.
To the original poster, a downstream injector just can not get the draw rate to apply a strong enough solution to clean roofs, unless you want to get a great Suntan!
Like everyone has already said, get a dedicated chemical pump.
As far as rinsing goes, on homes w/o gutters, it is always best to rinse the roof, then to play 'russian roulette', and depend on the rain. If it rains really hard after you clean a roof, you are usually 'home free'. But, when you get a brief, 1/2 ass rain, all that chit come off the roof, onto the plants, and then guess what happens ?
All that residual roof cleaning chemical (mostly salt), comes off the roof, w/o enough water to render it harmless.
Plants get compromised, customer get pissed, and instead of referrals, you get bad reviews.
However, rinsing a roof takes time, and the chemical needs to dwell on the roof for at least 30 minutes,, to insure all the algae is killed.
A great compromise to rinsing the entire roof is this. After you are done, simply go around the roof from the ground with a high flow garden hose, like the excellent "Mean Green" 3/4 inch water hose from Factory Direct Hose, and rinse the bottom 1/3 of the roof only.
If using Tarps, keep them in place during this partial rinse, or be sure and water the plants real good before, during, and after the rinsed chemicals are coming off the roof onto them.
Experience has shown this partial rinse will prevent complete plant death disasters, but it is still even better to rinse the entire roof, though it is quite time consuming.