Web app deployment strategy

Background/Context

I’m running a WordPress site on a DO droplet whose static js and CSS are generated via gulp tasks. For those interested, I’ll leave the contents of my gulpfile below. My entire WordPress site is stored on Github and I’m using GitHub Webhooks to auto-deploy new commits that reach the repo to my DO server.

Problem

I use SASS to facilitate writing styles (for anyone unfamiliar, SASS compiles to pure CSS). This is done via the compile:sass task in my gulpfile. Today, I need to run gulp locally and commit the built CSS file (style.css) to my repo so that the changes end up on my server. This is a bad practice and one I’d like to change. In an ideal world, should my server be executing gulp every time it receives a message from GitHub’s webhook? Are there additional build processes that I should implement to make my setup more bulletproof?