How is it possible that my expected time of arrival to the website changes?

The speed of the queue can be fully controlled which might increase or decrease the wait time. This affects the estimated time of arrival. In the case of increased queue speed, the estimated time of arrival decreases and in case of decreased queue speed, the estimated time of arrival increases. If a lot of people, who are in front of you in the line, decide to leave the queue, this will also influence your wait time so you will arrive earlier.  
The estimated wait time is calculated in a separate part of Queue-it infrastructure, not in the browser. The waiting room page reads this statistic, which tends to change only when the flow rate is adjusted or paused. If your internet connection is interrupted, intermittent or really slow, the refresh rate and displaying of the stats within the waiting room theme may not be instantaneous. But, nothing in your browser would affect the overall spot in line.