As far as I can see, your source for saying these two shouldn't be combined is a user on Reddit. That is not a reliable medical source. The package inserts of Ritalin and Concerta don't mention coffee consumption. This is interesting because
coffee being such a ubiquitous drug, you'd think if the combination was dangerous or discouraged, there would be easily available studies and it would be mentioned in the package insert of the medicine.
Most studies on the subject compare methylphenidate to coffee intake, because they are both stimulants, but there has even been a study where caffeine and methylphenidate were combined and given to children:
in which they received caffeine in low (158.6 mg) or high (308.6 mg) doses. Methylphenidate was added to both dosages, as well as administered alone. Results indicate that caffeine in low doses when added to methylphenidate was superior to all other treatment conditions and could not be differentiated from 10 mg of methylphenidate.
This was a really small scale study, though, with only six patients, which is not nearly enough to look at side effect. Or effects.
Now, caffeine and methylphenidate are both stimulants, though with different mechanisms of action. Methylphenidate effects dopamine transportation, while caffeine effects adenosine receptors. There is a good overview on this in the paper found by Susan, Psychostimulants and Cognition: A Continuum of Behavioral and Cognitive Activation, which compares the mechanism of action and effects of several stimulants. The section most relevant for your question is this:
At low doses, stimulants produce an increase in wakefulness, attention, and confidence and vigor. Drugs with low potency or maximum effect, such as caffeine or modafinil, act much like low doses of amphetamine or methylphenidate
This is why the study linked above was about combining caffeine with methylphenidate - seeing whether the dosage of methylphenidate can be lowered if combined with caffeine. It stands to reason that at one point, combining the two can lead to nondesirable effects because of too much stimulation. However, we don't seem to know when this will happen.
This is not medical advice and I am not recommending you go out and combine these two, or not do that, you should ask the doctor prescribing the methylphenidate that. But your source recommending against combining them isn't reputable.