This behaviour is normal for Delta Links running version 2 firmware. V2 was introduced to add compatibility with Pro Tools HD Native (and later HDX) cards.
The computer needs to boot fully and initialize its Avid hardware first, in order for the Delta Link, when it is switched on, to correctly identify the type of card it is connected to. If the mac is rebooted the Delta Link will need to be power cycled.
It is totally normal for this to happen, even when using older HD systems, as the Delta Link needs to be powered up last for the card identification process to work. The identification process is necessary because the Delta-Link interacts with the different cards in slightly different ways.