JSF date converters have a UTC time zone by default. But your date, apparently, is stored in the EEST time zone, which is several hours higher than UTC (more precisely, GMT + 3). When they enter these dates using the UTC time zone (as the default JSF), you will get the clock back in time and thus the previous day will be presented.
You need to explicitly specify the time zone in <f:convertDateTime> :
<f:convertDateTime pattern="dd.MM.yyyy" timeZone="GMT+3" />
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