The trick is that you need to make the list of Date type i.e. List<Date> (Please note that if your List is of String type, it will not work.
And 2nd important step is to use <f:convertDateTime pattern="dd.MM.yyyy" />
<h:outputText value="#{(<From the backing you are getting the date here>)}">
<f:convertDateTime pattern="dd/MM/yyyy" />
</h:outputText>
In your case it should be like List<Date> dateOfBirth instead of List<String>.
So in the form backing bean if you print the logs, even you get Date in format E MMM dd HH:mm:ss Z yyyy for example Tue May 21 10:47:34 IST 2019 thats ok and you need not to worry as this date will be converted to corresponding date format which you will convert by using <f:convertDateTime> in your xhtml file.
I tried this and it worked for me. Incase you have different solution please feel free to share :)
Detailed explanation : dateFormatter
dateOfBirthin the backing bean? - Yannick