I feel it is only a stopgap fix as we should have those items checked. I put in a request to Avast via a ticket, may I suggest you do also.
No, there is no should here, scanning encrypted connections is a bit controversial, the way avast does it is effectively by doing a benevolent Man In The Middle 'attack', inserts a root certificate in your keychain (randomly generated upon install) decrypts, scans the content of the connection and encrypts again using the Avast root certificate and sends that to your browser, it's a hack because secure connections aren't supposed to be snooped upon (which is what the avast proxy is doing).
So maybe in OS X 10.10.3, Apple has upped the security with the way certificates are handle, which is actually a good thing.
HTTPS scanning is off by default in Avast!, and for a good reason, I personally keep it off too.
The On Access Scanner should identify malware when it hits the disk.