TENNIES is short for TENNIS SHOES, which used to be the word for SNEAKERS/ATHLETIC SHOES. This may be specific to the US.

The only meaning of 'tinnies' I know is cans of beer or lager (not soda as far as I know). But this is Australian and the woman has an American accent. There's no context so unless someone knows another meaning if 'tinnies', it'd be impossible for anyone to guess. For all we know, it could well mean what you guess.