I've been thinking about the "lab assistant" familiar ability. It's worded similarly to megaton strike, where you use the action instead of your construct innovation.
To put it simply, your innovation strikes, but you take the actions (basically you overriding the construct's controls to attack something/someone with their strikess).
So my assumption is that lab assistant is your familiar literally acting as a lab assistant so that YOU can use YOUR quick alchemy quicker.
It's the only way for it to be useful, because if it's the familiar doing it, and that the alchemical item doesn't end up in either your hand or your alchemist's toolkit, it's genuinely worse than just doing the alchemy yourself.