Hi, connect your new iphone 6s to the mac pro with the USB lead and it should ask you if you want to restore from the backup. If it doesnt ask you can do it manually. It will probably ask a few basic questions before then and you may need to update iTunes first depending on what version you are running but try without updating itunes first.
The icon bouncing up and down is usually to get your attention about something, there may be a window hidden behind other windows that needs your input. If it is updating your iphone to the latest IOS it may take a bit of time.