I am experiencing and issue which is caused by the fact that your template loads a custom variation of font-awesome icons which no longer matches the standard ones.
Instead of having a standard icon-clock equivalent, the template provides icon-time, thus nothing to be shown.
Although I could override the class itself so that it loads your template custom icon, the time picker will most likely generate errors due to the fact that 2 entirely different Bootstrap versions are loaded by the template Vina Royal II..
Further to the component RSEvents!Pro has been designed to utilize the same Bootstrap Joomla! natively supports, this being 2.3.2. The calendar itself is the one provided by the Joomla! Bootstrap.
Hope you will update template to accomodate appropriately.