We have installed Piwik this week on various sites we have. We use 1 database for all sites.
On two sites Piwik is working great. On the other two we only get to see direct traffic. So no specification where the traffic comes from (referrals, search engines, social).
I think I found the problem.
Your Piwik runs under HTTPS only. Requests send over HTTP are redirected to HTTPS. While redirecting the parameters in the URL are encoded, which results in double encoded params. So Piwik can’t detect valid referer urls.
You should adjust your tracking pixel to https always. You currently use protocoll-less urls (//domain). Simply add https: there.