Ding! That was my guess. Kind of like teacakes, teacookies, te biscuits, etc... are consumed with tea, but don't have tea in.
Now, the cake part... I've seen coffee cakes, the muffin sort you're eating is probably a miniaturized version of the coffee cakes I know and love.
The coffee 'roll' I would think of as a roll because it's made of a long strip of dough rolled into a spiral shape.
Sort of right Bliss.
Tea cakes, (which are actually a bread 'bun' made with mixed fruit and are usually toasted), tea biscuits and most other things that are so named, are named after the time of day they were eaten, not just because they were eaten, as an accompaniment to the drink of tea.
There was afternoon tea at 4pm, (that the middle classes had to stem off their hunger for a later dinner) and high tea between 6pm and 8pm,(for the middle classes to have if they needed something substantial before going out in the evening and would eat, say after the theatre, a supper) or, if you were working class, high tea was the main meal of the day.
I still call our midday meal 'dinner' and evening meal 'tea'....*smiles*http://www.woodlands-junior.kent.sch.uk/customs/questions/food/tea.htm
Morning coffee, on the other hand, was a very middle and upper class thing, (working classes didn't have time to stop for a meal then and they certainly could not afford coffee) and foods that were eaten at that time, had the prefix 'coffee' attatched to them.
(However to completely confuse the issue, we do in fact have cakes here made with coffee as a main ingredient and the same goes for tea)