Response from Andrew, Alfred's dev:
You have a few options, the easiest being setting Alfred's Appearance > Options > Focusing into Compatibility Mode, which will make Alfred operate like a standard window (instead of floating panel). BTT should be able to know Alfred is visible.
Secondly, you can make Alfred publish events when things happen by enabling his "Press Secretary". Take a look at my post here which discusses how it works, and what is posted:
I've implemented compatibility mode and it's resolved my problem immediately. It might be interesting for you to look at Alfred's 'press secretary', though, to see if it's useful in relation to BTT.