Not sure about the terms used in dim sum, as a tick-sheet is a tick-sheet! But certainly for many Singapore street food dishes, the name of the dish tends to be referred to in Hokkien Chinese rather than Mandarin. I kinda agree with your multilingual theory but that's a product of having a population of mainly southern Chinese in a small city.

In China, it's more likely that local people will use local language/Mandarin for dim sum as language spreads with people. And with the possible exception of Shanghai, there are few cities within China (outside of Guangdong) that the Cantonese migrated to. By contrast, cities like Singapore and Kuala Lumpur have sizeable numbers of Cantonese for their food terms to seep into common usage.