My cockatiels are refusing spoon feeding - help!

As a preface my two cockatiels are 5-weeks old, and I feed them approx. every 3-4 hrs.

I began the weaning process yesterday. I put bits of wholegrain toast in their cage, and after we soaked it overnight (aka this morning) we introduced millet. We switched to spoon feeding instead of the syringe yesterday as well. Luna took it well, makes sense since she's a few days older. She eats from the spoon (although slowly, and not until she's full) and investigates the bits of food in the cage. Tina, however, refused to eat from the spoon at all. Today morning she looked so frail and felt bony I reverted to using the syringe. She slurped it all up gratefully.

I followed common advice and fed them whenever they're hungry, but now it seems like they're hungry all the time because they don't eat well via spoon ...

My question is: does it matter if I feed them by spoon or syringe? I was thinking that maybe the spoon will help them be less dependent on someone else for food, and thereby ease them into weaning ..? Or does it not matter? Because I noticed that the quantity they eat has gotten noticeably less, especially in their weight + appearance ... even though it has barely been one day.