Email not sending when products are updated through 3rd party plugin

Hi all!
I love your plugin and implementing a way to let people enter their email works like a charm.
However, the client Im building this for uses a third-party inventory management plugin to manage their stock.

I have tested all sorts of settings and nothing seems to work. Manually sending the email works and it also works when I change the stock in WooCommerce, but when I change the stock in the other tool (it’s called SW Retail), the e-mail is not sent.

I have the following settings:

• Checked ‘Enable this option if you have updated the stock from a third-party inventory plugin’
• Background process engine: WooCommerce
• Checked ‘Consider Only Published Product Status’

I do have a lot of other background processes as well.

Is there anyone that has any idea what the issue might be?