The JSF date converters defaults to UTC timezone. But your date is apparently stored using EEST timezone which is some hours beyond UTC (GMT+3 to be precise). When intepreting those dates using UTC timezone (as JSF by default does), you will get hours back in time and thus the previous day will be represented.
You need to explicitly specify the timezone in <f:convertDateTime>
:
<f:convertDateTime pattern="dd.MM.yyyy" timeZone="GMT+3" />