I am not sure if this might be your problem but I had this same issue and posted a thread about it. I got the same answers from all the alidropship team that it "works for them", but what they didn't tell me was I needed the
'Shipment and Tracking' extension for
'Woocommerce'. Without it, there is no field inside the orders for a tracking number to be placed (and since woocommerce is what deals with all your emails you need it). You can either purchase the subscription from woocommerce directly (billed at $49 per year), or you can download it for free from
https://gpldl.com/repository/premium-woocommerce-extensions/ (credit to user DirectWebstore). Once you install it, the orders screen will no have a Shipping field that allows you to insert tracking numbers and the courier service used (which the Alidropship plugin will do automatically when synced with Aliexpress). And if the Alidropship plugin cannot do what its intended, the email just doesn't work.
You don't need to worry about it being illegal, in fact all of wordpress plugins are 'General Public Licensed' meaning the actual plugins are free to use, you are literally only paying for support and updates, so you don't need to pay the subscription to actually use the plugin. You just won't be able to receive any kind of support or updates unless you purchase the subscription or wait for GPLDL to update their list (usually a few days after the update has been released).
I think the main issue the Alidropship team has with these kind of support questions is they assume you are 100% experienced with woocommerce and that you already have the necessary extensions for their plugin to work through woo. But in reality, a lot of the users using the woo version are doing so they aren't limited to themes, or functionality that woocommerce can do provided they learn/know how to use it.
Another issue could be if you're using your hosting provider as your email service. A lot of issues can arise from that, there are plenty of blogs out there that will tell you why not to use your hosting provider as your email host with a simple google search. Hope this helps and I hope you can get the issue fixed as soon as possible.