The Google Job Search Integration was added in version 1.28.0.
WP Job Manager will automatically include structured data about your job listings on every individual job listing page, using the JobPosting schema type from schema.org. This helps Google and other search engines understand certain information about your jobs, such as the type, the location, the name of the employer, and so on.
It includes the proper schema for making your job listings compatible with the Google Job Search requirements, but it doesn’t automatically submit your jobs to Google. Google will eventually crawl your site and find the jobs without any action on your part, similar to what it does with sitemaps. If you like, you can try using a SEO plugin to help you with automatic submission of your jobs to Google to speed up the process. Any questions about this would need to be directed to the support for that plugin.
You can use the Google Search Console to check that there aren’t any issues with your site’s structured data.
We have some documentation on fixing structured data issues here, if anything shows up when you check.