Not familiar with this box directly, but looking at the specs on the Black Magic web site, it doesn’t mention anything about downconversion of HD to SD on playback. You are right. Your switcher doesn’t support HD signals, so my guess is that the component signals you are feeding to it are (should be) HD analog when your timeline is HD, which the switcher can’t use. Most Black Magic cards/devices should have software to control the device. It’s often in the preferences panel on a Mac. You might check there for additional controls. See if there is a box to enable the downconvert function, if it exists. I know the Decklink Extreme card has this feature and a control for it.
I’m thinking that for the price point of your box, it might not have the ability to downconvert, but this is purely a guess.
E=MC2+/-2db