OrderlyEmails does not actually send any emails itself, nor trigger the emails to be sent. The app is a design tool that upgrades the emails that Shopify is sending for your store. Therefore, your store continues to work exactly the same as before, just now with much better email designs.

This means that we cannot see why your emails are ending up in Spam, as we aren't sending the emails. However, one common issue which can cause bad delivery in general is something called "email authentication". 

When an email is sent, the receiver will check to see if the sender of that email (Shopify's servers in this case) is allowed to send email on behalf of the email address domain (yourdomain.com). Email systems check for something called a DKIM or an SPF record setup with your domain provider. Think of it as a way to tell the receiver of the email "Yes, I know Shopify's servers are sending emails with my domain as the sender, and I'm cool with that". In your case, it could be that they are not finding those records and so see the email as potential spam and don't deliver them.

Shopify does not support the more recent DKIM records, but they do support SPF. It's something that you set up with your domain host (where you purchased your domain). Shopify has a guide on the details that need to be setup in your domain here: https://help.shopify.com/en/manual/intro-to-shopify/initial-setup/setup-business-settings#add-shopifys-spf-record-to-your-domain-host-custom-domains-only

The Shopify Support team should be able to help you out with getting that setup, if needed.

Once the SPF record is set up, then your emails will get through to inboxes much easier, as you have essentially verified that the emails being sent by Shopify are legit.