Safari - saved favourite that became https still shows as http

Hi,

my own website recently had an ssl certificate applied. It was saved as a favouite on my safari but would not show the https until I unsaved it then saved it again. Does this mean that all my clinets have to unsave/save it to show the https? There is only one website so I presume if this is also happening to them they are actually logging on to to https but it just isn't showing as such?

JCC