Given Trellis creates DB tables in development, it can be surprising that …
Trellis does not automatically install WordPress on remote servers. It’s normal and expected to see the WordPress install screen the first time you deploy. It’s up to you to either import an existing database or install a fresh site. – deploy docs
Deploying is a process you will repeat many times as your site evolves and updates over time, whereas importing or creating DB tables will typically only happen once, after your initial deploy. So, the deploy doesn’t automatically create/import tables.
If you notice a great place to make another mention of this in the docs, feel free to submit a PR.