Sure, red cabbage juice exhibits quite a marked indicator effect. Bicarbonate of soda is alkaline and lemon juice is acid.
I don’t think that’s how this was done, however, as the colour is apparent immediately as the liquid exits the bottle. Indicator chemicals would take a short moment to change, especially if the acid/base was coated on the spoon.
It’s a flattish bottle and we never see the side that starts off facing Mary’s chest, against which her thumb is pressed. It would be fairly simple to conceal some mechanism in the bottle that is operated by the thumb - in simplest form: three pipettes glued in place, accessible via a cutout in the unseen side of the bottle.
When I quickly glanced at the video, the liquids’ flows seemed a little off: they seemed to start too late and end too quickly to be coming from a half-full bottle tipped over, more like as if something inside the bottle releaded one spoonful of liquid at a time.
That bottle was so freaking huge that I always guessed as a child that there were three bottles inside of it, each with the different colors - in retrospect, tubes would make more sense and be easier. 
As far as child actors and genuine reactions go, one of the nicest I’ve seen recently was the actor playing Lucy going into Narnia through the wardrobe.
Everyone was under strict orders to keep her away from and unaware of that particular set, so the shot we see is truly her first sight of it, and it’s a beautiful thing. I don’t know, but it seems to me that not many young child actors would be capable of producing something like that on command.
I think I remember this being discussed when “Star Wars” first came out. There was a great deal of talk about the light-sabers and how they were “put in afterwards, like the medicine in Mary Poppins.” I’m not sure what that meant exactly, but I assumed at the time the film had been individually exposed for the necessary scenes in order to produce the effects.
IIRC (can’t see Youtube from work) the liquid in the spoon has a slight “glowy” look to it, as if it were brighter than the surrounding scene. It seems that re-exposing to produce a brighter effect would be fairly easy. I don’t know how they copied films in those days though. Would they have been able to do this once to the original? Or would they then have had to do the same with every copy they made?
Well, the film already contains lots of effects applied after shooting, but the coloured medicine thing seems a fairly simple physical trick - I’ve seen TV Magicians do almost exactly the same trick.