The seo experts told us to put rel="nofollow" to all external links.
Trying to massage PR (for want of a better term) in this way sounds like a very outdated concept to me. Is e-Commerce any different in this respect? If a site is worth linking to it should be "follow".
rel="nofollow" should only be used on paid-for or untrusted (ie. user-submitted) links. Unnatural links or links that only serve to advertise (comparable to "paid-for") should also be
Should I put rel=“nofollow” on author link?
I would consider adding
nofollow to your site backlink. This is of low quality anyway and is unlikely to count positively towards your sites SEO. As you openly state, it is "a little advertisement" and therefore unnatural. The reason for this link is to simply to allow the few site visitors who are interested to find out the developer, not to directly benefit the developers site SEO. If you notice on the "best" sites, they don't include such a backlink at all.
In the following Google Hangouts (at 32:35) from 5 May 2014, John Mueller is asked a similar question (backlinks to developer's site in footer) but on a much bigger scale. tl;dr It's safer to use
nofollow on these links.