What romulus said. As for the grammar, 'tuck-ins' are "things you tuck in" (clothes, in this instance); like "carry-ons" = thing you carry on(to a plane).

it means to gather up and fold, thrust, or turn in so as to secure or confine: e.g She tucked her scarf into her blouse. cowboy...

the main verb actually is "tuck". "tuck-in" is basically fitting your shirt into your pants or skirt, leaving no shirt tail seen outside. the shirt being mentioned in the website you've visited does not necessarily need to be tucked-in (as what a baggy clothing are designed for). :)