As of SCD 2.7.0, there is an option to autoquit SCD when using the browser extension. If you have SCD closed and click the download button, SCD will automatically open and as soon as the download is complete, it will automatically quit.
You can find this option in the settings under the general tab:
Please note, that this is only a donator feature! If you haven't donated yet and would like to use this option, head over to black-burn.ch/donate to get yourself a key for SCD!