I like my MO... I start with a Leslie's water test container and a 2.5' length of PVC. I hold my thumb over one end of the PVC and put it down into the pool. I release my thumb and let the PVC fill with pool water from 2' deep. Same place in the pool every time. I then fill the container with the pool water from the PVC. While I'm dipping the PVC back in a second time, to repeat the process, I'm shaking the container out into the pool. This effectively rinses both the PVC and the container. The second "fill" is what I test.
I then fill whatever I'm testing with with the water from the container, and shake and rinse each of those thoroughly. So note, I'm rinsing everything before I test with a fresh sample of the pool water, NOT with water from any other source, especially tap water.
Some here will do one or more of those steps repeatedly. One guy here rinses everything three times.
Then I perform the test. I do all this every time, consistently, and so get consistent results.
Your "first drop" theory is plausible, can't hurt to try tossing that first drop. But the test chem's manufacturer doesn't include that in their instructions, which leads me to believe that it's not necessary. Though maybe your tip is clogged or something? Try replacing it. The whole vial, not just the tip. Be careful if you're tempted to try and clean it. Don't poke anything through the tip's hole, those are calibrated and you don't want to change its diameter. When I have to handle those tips, I don't even touch them. I use a lint-free cloth between my fingers and the tip, thinking I might contaminate the tip with dirt or oil, whatever. I treat those tips like surgical equipment!
The keys: fresh testing chemicals; rinse everything thoroughly; and use consistent, repeatable, careful, clean testing methods...