Hi,
So first, I've activated the saving of the cron report in the settings of the HikaShop configuration, so that we can easily check what's going on.
Then, I triggered once the cron, and I didn't get any information about the reminder plugin in the report.
So I checked the settings of the plugin and I tried reducing the frequency to 1.
Then, I tried launching the cron again but I always had the same report displayed on my browser, without anything logged in the cron report. This indicate that there is something on your server caching the result of the request and sending back the cached version instead of processing again the request. I confirmed this by adding an extra parameter to the URL of the cron, and when I did that, I got a new cron report with the reminder information in there:
No created order left for remind notification
No cart left for remind notification
So the issue I believe is that caching mechanism. Because of it, the cron is not properly triggered each time. Only when I add a new parameter to the URL. You can see in the report of the cron that it only triggers when I manually open the cron task URL and add an extra parameter.
And with the normal URL, I still get the first report from 20 minutes ago.
So you need to check the caching on your server to exclude the cron URL and it should then work properly.
Now, it still seems strange that no cart / order are being found to be reminded. I suppose it has something to do with the settings not properly saving because you configured the plugin to send an email when a cart is more than 15 minutes old while no orders having been made since then. And thus, that should definitely trigger some reminder emails as I can see you have carts fitting that situation.
I would need a FTP access to check things further on that end.