It sounds like you need to use an HTTP certificate that your browser accepts and/or you're using the wrong port. In the case of the certificate, the extension is not capable of letting you add an exception like you can in normal browsing, so you need to specifically accept your certificate browser-wide for it to work.

If you file at issue, I may be able to fix it.

https://github.com/seansfkelley/synology-download-manager/issues/new