What is your pH meter reading? Are you calibrating it with buffer's of known standard concentrations? Buy some distilled water in gallon jugs from the grocery store, DISTILLED, not filtered, and that should be about as pure a water sample as you need for what you are talking about. Take the pH, then pour it into your containers and let it sit for a few days, again take the pH.
I wouldn't say it matters how "perfect" your pH water measurement is, as long as you record it before hand, as any change can be attributed to the new container. Also, I'd take one more quick measurement before you put the cap on the new container in case the mixing action added extra carbon dioxide and lowered the pH...still, I think the change will be very small and perhaps negligible.
pH meters DO often go crazy, so you usually put it in your sample, count to 15 seconds, and take the reading. Do this consistently with all readings.