ekko's e applies on-attacks effects like stattik shiv or rfc before the autoattack itself

I don't have a video, but it's really easy to reproduce:

Step 1: Play Ekko and buy Stattik Shiv/Rapid Firecannon Step 2: When Stattik is available, use your E and attack a minion

I done well, your Stattik Shiv proc should come off before your autoattack even launches (even before you blink)