When I search “fingertip controls” it comes up with examples of push buttons so I’m not really sure what they might’ve meant!

I’m thinking it might’ve just been more advanced or complex than a simple on/off switch, like a series of dials or buttons or one single button that could have been used for multiple settings.. for example with cars - a starter, windshield wipers, headlights, an accelerator and brakes etc all in one button or panel? For a chair, it would recline fully, partially, or lift you back up. Maybe the different settings on a hand mixer, dishwasher or a washing machine? 

But that’s just a guess! 

Whatever it was, it doesn’t look like it advanced very quickly, take this “fingertip control” from the Dixon Evening Telegraph, Illinois, December 11, 1967…

This might be more what the article had in mind.. Jefferson City Post-Tribune, Missouri, August 14, 1968:

“She will have in her kitchen a small television screen and a console with a number of buttons.”