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A poor sealing quail is a source of angst for many drivers. The sure do look pretty but require a good job of fitting and adjusting to make them seal properly.
You should not get water out of the cap with the temperatures you are stating. It should be pushing out the overflow tube.
How full are you filling the radiator? If you are adding coolant and filling to the bottom of the neck you are probably filling to far and it will push excess coolant out due to expansion as it warms up. A poor fitting quail will spit coolant in a hurry.
Don't add coolant unless it no longer covers the tubes. As long as they are covered all is good.
I'm glad your using a 50/50 mix of antifreeze and distilled water. It will help it run cooler, prevent rust and protect against freeze damage.

How are you measuring the temperature of the coolant?
I use a cheap dial meat thermometer placed directly into the coolant in the radiator. The quails get you "close" but the thermometer puts you spot on.
Get one of the meat thermometers and you will know for sure.