Modern teak decks are decorative teak laid over a sub deck of fiberglass or other construction which forms the structural support. The traditional decks are planks of teak laid over a frame where the teak itself forms the structure of the deck. Re-caulking of a decorative teak deck is only necessary when there is physical deterioration of the caulking to restore appearance and to stop water damage due to trapped moisture under the wood. Re-caulking of structural teak decks is a continuous process which commences about 10 minutes after the deck was first laid and continues until the boat is abandoned. Teak should never be laid over steel plate decks. Inevitably the teak seams will leak and the trapped water will rust the steel causing it to swell and lift the teak off. On steel boats where deck webbing creates some areas where teak has to be laid over flat steel, the webbing should have as many holes cut in it as possible to allow water to escape and air to dry any cavities.
Traditional teak planks have cotton pounded into the seams when they are laid. This is quite an art and there are very few artisans left who can do it properly. The cotton serves a number of purposes. First it tightens the crack to minimize movement, and make the deck more contiguous. It seals the bottom of the crack so polysulfide (caulking) will not run through later. It is under high compression so it expands and moves with the teak when it moves. It absorbs water from a leak and swells to stop the leak. With modern polysulfide caulking compound I have found that pounding cotton into a seam while making repairs makes little difference and is not worth the trouble. If you have a crack that goes right through from a seam, by all means pound some in to stop the polysulfide running through (or tape it underneath with duct tape if there is access).
A groove is cut out of the top of each of the cracks between the planks to provide a cavity for the caulking compound. There are many schools of thought on the best shape of the groove cross section (width, depth, round, Vee, or rectangular) but here is my analysis. Teak deck caulking fails nearly always due to the caulking pulling away from the sides of the groove when the teak shrinks (dries out) and/or moves while underway.