Unfortunately, no. Bit Integration only triggers WordPress-based events. However, if Tidycal supports webhooks, you might be able to use a webhook to connect with Acumbamail.

We're working on an advanced integration plugin with a flow builder, triggers outside of WordPress, multi-step processes, routers, filters, and more. While it's a WordPress plugin, you can think of it as a self-hosted version of Zapier. Check out more details in the comments of this post:
https://www.facebook.com/groups/bitapps/permalink/5310065002338944/