Is tea/ caffeine harmful in any way to a person who has asthma?

Depends. These taken in moderation do not trigger or aggravate asthma.They both contain chemicals that are cousins of an asthma medication used years ago.(theophylline) As with any indulgence, excesses can lead to health problems, but these would not be specific to asthma sufferers.
Yes. Too much caffeine can affect the heart with rapid heart beat. Too much caffeine can upset the stomach with irritation. Too much caffeine can lead to dehydration from urinating. Caffeine does help dilate the airways in patients with asthma, but should also be taken in amounts that doesn't cause the above mentioned side effects of taking too much.