You can't compile your code automatically like you did before with the first version of the Eclipse plugin. The new plugin makes use of the [Language Server Protocole](https://github.com/Microsoft/language-server-protocol) which will help you find errors locally, but you'll still have to use `sfdx force:source:push` to compile everything.

If you have access to the Trailblazer Community, there is a thread about this [here](https://success.salesforce.com/_ui/core/chatter/groups/GroupProfilePage?g=0F93A000000HTp1&fId=0D53A00003DkTtM).

Additionally, you can automatically push your changes to your Scratch Org using Nodemon, as described in [this blog post](https://ntotten.com/2018/01/17/using-nodemon-to-autopush-sfdx-project-changes/).