In 1481 King João II sent his man Diogo de Azambuja to Guinea coast to establish the fort São Jorge da Mina, later known as simply Elmina, to fortify it's position in Equatorial Africa. Famously the fleet took with all the necessary materials for the fort, most importantly the previously cut stones for the walls, with also wood and other materials, together with at least 100 skilled workmen to preform the actual "assembly" of the prepared materials and construction of the fort.

I am not sure on details of how exactly the construction proceeded, but this illustrates one of the options the Portuguese utilized when constructing fortresses far away. Simply prepare everything in advance, bring your own workers and craftsmen, sail where you need and build the fort as quickly as possible. They did this again in 1522 when building the fortress on island of Ternate, in the Spice islands when they wanted to secure it against possible Spanish incursion in the wake of Magellan's expedition. I again know no details (like even what were the materials used) but again sources tell the story of everything being prepared in advance carried to the location and than hastily built.

Now, the two examples previously show construction in remoter areas, like you describe "jungle" and "small villages" without much support. But I just want to make it clear, the vast majority of Portuguese fortresses were done in major cities and trade hubs, with much possibilities of utilizing local resources and workforce, like in Goa whose skilled artisans were praised by the Portuguese leaders like Afonso de Albuquerque. In most instances, however, the initial fortress would be built by Portuguese men and soldiers as quickly as possible to entrench their position, and from there on use local craftsmen to build the rest, like in Cochin where the initial fort was a simple moat and wooden wall fencing of a mini-peninsulaand rest came later. This utilization of Portuguese men and soldiers could cause some unrest among the Portuguese, as for the example the aforementioned Albuquerque in 1507 tried to build a stone fortress in a strategic trade hub of Ormuz, his men refused to the work which forced him to retire from the area (later he returned and rebuilt the fortress).

Building of forts in cities allowed to use the materials already present, in one form or another. In another famous example of fortress construction, when Albuquerque conquered Malacca in 1511 he ordered a stone fortress to be built. For materials he ordered the local mosque to be brought down and it's stone - and also apparently stone from tombstones of previous rulers - used for the new fort bringing Portuguese dominion over the area. In Diu, Portuguese mostly entered and modified a pre-existing fortification.

So, all-in-all, Portuguese used different methods to build their forts. If the area was inaccessible, prepare needed materials in advance and head there. If the area was already a settlement of a enough size, secure your position and build a temporary fortress as soon as possible, and then slowly and steadily build a larger one using local or imported workforce and materials (but generally not Portuguese).

Here is an album of Portuguese forts in Africa and Asia in 16th and 17th century for those interested how they looked like. Naturally some of the images are of quite developed forts which took quite some time to be built in that condition.