Maybe this is the answer to my own question: From 2 sections of the rules of my game::
" The days and times stated herein are those of the UTC +01:00 time zone (Brussels, Copenhagen, Madrid, Paris). No other time zone will be taken into consideration for participation in the competition."
" Participants can log onto the website every day from 10am on 11th January 2018 to 10am on 21st January 2018 inclusive "

So that would be from 4am to 4am in NY.

Also, re: my other musings:

“Instant wins” are “open”; in other words, the prize is available at a precise time and remains available to be won until such time as a player has won it. Participation in the “instant win” is triggered by clicking on the "Play" button. When the participant has finished playing, and irrespective of whether or not the participant successfully completes the game that day, a screen automatically presents the “instant win” prize. One hundred and twenty (120) people can win an instant win prize each day, chosen by the “instant win” mechanism, making a total of one thousand two hundred (1200) winners over the course of the whole competition.