My experience is that many singers don't have much idea of chord structures or listening to chord changes. More usually they'll expect a consistent tune and come in at a preset point in that tune. Vary the tune and they're stuffed. Or they'll count, and if you double the length of your solo then again they're stuffed.
How bad is it, I guess is the question? For figuring out when to come in, "mechanical" is *good*! Singing with feeling is nice, but you can't add feeling until you've got the mechanical basics. And you'll need to be 100% mechanical as the backing too.
First question - can she hear a beat? If you play the backing for something with a simple rhythm like "Wild Rover", can she clap on the beat? If she can't, you've got a *lot* of work ahead of you, and she probably needs a professional teacher who knows how to help her with that.
If she can do that, could you cue her for the singing, by giving her something to shadow - so for Wild Rover you'd start playing and then you'd sing "one-two-three-one-two-I've..."? The singing then starts on the beat for her. Then you can stop singing the count when she doesn't need it, but she'll still have it in her head.