The Solar Bulletin lists the daily counts ; but how is a "day" chosen ? Us observers are scattered across the globe and individual counts will be made throughout the 24 hour period . This will affect spots leaving or entering the solar disc . I remember the late (and sorely missed) Tom Cragg jokingly telling me that he could make counts for two consecutive days only an hour or two apart from his home in Australia as he was so close to the date line .
So, how is this handled ?
I'm not sure if I am answering your question or not, but when you use SunEntry, you should be submitting the time and date in UT. This calendar date is then converted to JD (which starts at Greenwich noon) and the daily Ra numbers are computed simply by using the integer of the JD.
Also SunEntry is suppose to check for and not allow anyone to submit two observations that are made less than 12 hours apart. So tricks like what Tom Cragg mentioned (i.e. jumping back and forth across the International Date Line) should no longer work :)
I hope this helps,