Well it's pretty simple. Because the link is unique - you wouldn't have been able to find it unless you either watched her youtube video/instagram post/tweet or whatever.
Here's an example of a link that someone I watch on youtube left on one of her most recent videos;
https://www.youtube.com/redirect?redir_token=7_RPNBMKE8kKira-NnMRpODBKVZ8MTUwNTMxMjE4OUAxNTA1MjI1Nzg5&q=http://bit.ly/2vMHAHX&event=desc
however on youtube it's shortened to:
http://bit.ly/2vMHAHX
These aren't things that the average joe will just type in, they're designed specifically to notify the sponsor that this particular youtuber has referred x amount of people to the site.
The banner ad will have it's own unique identifying link, that isn't tied to the youtuber at all - so it's easy to trace that also.
As for whether marketing influences your decision, only you will know whether you are not influenced by any branding, advertising or marketing at all - but there's a reason why its a multi-billion dollar industry globally, and you've got hundreds of people getting paid for simply advertising things on youtube.
Word of mouth and recommendations carry weight, potentially more so than commercial marketing, and youtubers are helping brands establish themselves simply by pushing certain products.