That is an issue with the data for Dead Eye, where it's not flagged to trigger augments. It should be a simple fix, so I'll see if that can make it into the next update.
Just realized this also affects his future basic, Calibrate, as well. :S
Do any other toons have this issue as well where 3-tap basic attacks aren't flagged to trigger talisman augments? I fear he may not be the only one.