Tyrande, If the Dell command update is installed you do not require to check your update through the Support assist as the Dell command update has a higher priority and may cause the SA updates to be redundant.
I have both Dell Update and SupportAssist installed on my Dell Inspiron 7579. Even after updating my laptop using Dell Update, the same updates show up when I start SupportAssist. SupportAssist should have a way of knowing which updates have already been installed on the laptop.
SupportAssist is displaying updates already installed by Dell Update