Time displayed on the NIST time widget is seen to agree with the file's Modified time given in MS Office Picture Manager in the image below that was used to sychronize the camera's clock with the official time. So the best procedure may be to synchronize these two times.
The times used can vary by a second or two. Network Time Protocol is used to synchronize clocks over the internet. W32Time is used by some Windows computers to set the System Time for the computer. NISTIME 32 appears to use this method. The time zones are based on Universal Time (UT) which is adjusted periodically to maintain a correspondence with the Earth's rotation. The error is known as ΔT. We are due for a correction to UT1 in about a month from now on Jun 30. The times given by MICA for the eclipse use UT1. This may be a partial explanation for the problems encountered.
Above is a comparison of some of the times obtained by different methods showing a range of values. The times shown will depend on the time the image is captured.