You are probably giving them too much credit to think they were all of similar design, especially because for the most part we today have no idea how medieval and late medieval ships looked like in detail. Most likely (as recorded) they all varied in design, usually reflecting the local shipbuilding practices of their place of origin, with only the key features purposefully made similar.

So tracking spread of ships design back then is hard, additionally so because there really wasn't any ship design, at least not in sense of blueprints and writings and drawings. Most shipbuilders made ships without any plan, at least until late 1590s, and even after that it was an uphill battle to get shipbuilders to record and use blueprints.

In those conditions the simplest way to build a ship of a new type, was to hire the shipbuilders that can build it. For example of caravels, per Martin Malcolm Elbl Philip the Good, Duke of Burgundy had a caravel built by "an emigrant Portuguese shipwright" who settled in Flanders. Philip the Good was married to Isabella of Portugal, daughter of Joao I, founder of Avis dynasty, and through her Burgundians and Portuguese had really good relations, and could more easily go about hiring such an expert, whom the Portuguese guarded jealously and rarely allowed emigration.

In the absence of possibility to hire such experts, the other option was to reverse engineer the ship obviously. You could use a ship captured through piracy or sequestration, or simple legally buy it from the owners like any commodity. Portuguese Kings in the early 15th century promulgated a series of decrees forbidding the sales of their caravels to English buyers, exactly to prevent the spread of their technology. The prohibition was naturally almost impossible to enforce, as ships were regularly bought and resold, so soon English, Scotish, Flemish and other had their own "caravels", which of course had their own distinct preferred characteristics. For example while Portuguese preferred Lateen rigged caravels, northern ships usually sported square sails.

Even if a ship could not be bought, it wasn't a problem to observe the ship and copy or imitate it's features. After all ships were carrying cargo and people from location A to location B, so it was naturally that men in the new location will see the new design. Through local shipbuilders making minor repairs, through loading and unloading of cargo, through customs official inspecting the ship for contraband and for customs duties, and ultimately through passengers and hired crew which had no reason to keep anything secret, information could be easily obtained on the ship peculiarities of design and the opinion on the performance. So ultimately it wouldn't be a problem to gather what is the new feature and what does it bring, after which it was only up to local skilled craftsmen to be able to implement this on their ships. Which - going back to the beginning of this comment - they often did with considerable variation.