Mine had the same trouble on the thumb push lever – had to flick it back with my index finger after shifting. It was sticking due to general kak buildup inside the shifter. Undo the screws you can see on the outside and take the top of the shifter off (nothing will pop out unless you pick at the mecahnism), pick out anything obvious (being careful not to dislodge anything that may pop out), squirt with some flavour of lube, reassemble, whizz up and down the gears a few times to work the lube in and all's well.
The cables were fine as evidenced by the perfect shifting after lubing the shifters.