The natives are wearing flowing toga-like robes of white cotton or linen, and the Dutchmen are wearing what look to me like stiff, all-covering uniforms of itchy wool, along with tall leather boots.
How did they not all drop dead of heat stroke? It always baffles me how back in the day, Europeans would go around in tropical climes dressed as if they were taking a stroll along the Baltic. I myself sweat half to death on days when I am forced to wear a suit if it's any warmer than a Greenlandic summer.
It will be good to see an example, first of all because it depends on the location and time, and second of all because paintings are often not exactly accurate representations.
Otherwise, yes, of course heat exhaustion is a major concern when you are in an archipelago on the tropics.
It's not specific to Dutch soldiers, but How Were Uniforms Modified by Soldiers has some wonderful discussion on the topic of dealing with uniforms in different climates. Keep in mind as well, that the use of synthetic fabrics is very recent and those are by far the most likely culprits in clothing being hot and unbreathable (your suit lining being an example). On top of that, they don't have air conditioning and will acclimate far easier than a modern person going through the shock of temperature changes. That doesn't make it pleasant, but it's better than you think.