All the while assuming that they were navigating on a sphere, of course. If they had known they were sailing on a disc, their maps would have more closely resembled the actual shape of the continents they were navigating.
But the maps represent what was actually observed whether they assume a spherical or flat Earth. The charts were based on distances, courses steered, bearings measured and depths measured. Measurements of latitude were the first piece of positional data that were added. Longitude was still based on the information used for dead reckoning their position (distances, courses steered, bearings measured and depths measured). This accounts for the east-west stretch of late 16th century charts.
With the invention of the chronometer, accurate longitude information could be added to the chart. This is when you start to see what is considered an "accurate" chart of the globe.
Why go through this description of the evolution of charts? To point out that charts were based on information that wasn't prejudiced toward either a spherical or flat Earth. This information was plotted as it was observed, not to fulfill some mission to prove the shape of the Earth. You measure a course and distance between two points and place that on the chart. You verify that location using celestial observations, and that makes the charts more accurate.
In my opinion, the fact that the information collected led to charts that demonstrate consistency, shows something about the nature of the Earth, but the information itself is neutral.