To look how each siege resulted, the safest bet would be to look at each battle independently and judge just that one. However due to brevity of space we may make some broad conclusions.

First, to address the specific example, the attack on Chaul referenced was part of 1571 "War of the League of Indies" when in a very rare instance, multiple states attacked various Portuguese holdings at the same time. Chaul attack was one of those, but it wasn't by Ottomans, but by forces of Sultanate of Ahmadnagar , one of the Deccan sultanates. While the army had people of Turkic (Rumi) origin, it for sure wasn't an Ottoman force. The number, while it is given by some primary source, is also probably too large , usual estimates are in the range of 30-60,000 at most, which is still huge.

Now to speak more generally about sieges involving Portuguese. Portuguese were most of all very experienced in siege warfare, in both taking and holding forts. Even before reaching Indian Ocean, throughout the 15th century, and well into 16th Portuguese were constantly engaged in back and forth battles over coastal forts in Morocco, taking them and holding them against the usual counter siege. Not every case was successful for the Portuguese, but often enough that more then one historian wrote that Morocco was a "school" for Portuguese empire building in India.

Even if that is an exaggeration, reality was that Portuguese were quite adapt in design and construction (and fighting) of the forts. Given that all their forts as a rule were coastal fortresses, and as Portuguese practically had naval supremacy, the forts could always be resupplied and reinforced by sea, preventing one of the main requirements of a siege: breaking the besieged supply lines. More so, Portuguese forts were usually in positions near rivers or islands or bays, and while defending them Portuguese could and did move ships around and use them as firing platforms to harass the besieger, or to launch sorties into enemy weak spots.

To put it short: Portuguese were very experienced in this kind of amphibious warfare with combined arms: melee, firearms, cannons, ships. At the same time their opponents were coming from completely different background. Indian armies were mostly orientated towards cavalry forces ( with occasional elephant units ) with less accent on siege warfare, and almost none on naval combat. By the 1571 and siege of Chaul, they would get plenty of experience, as well as good cannons, but seemingly not enough to end the siege in time.

Which is the final relevant point, campaigns in India were limited in time by seasons. Once the rain season starts, it's basically end of campaign. So much rain, it makes it impossible to do any real military action. So Portuguese only had to resist long enough and the siege couldn't last indefinitely. Forts properly built, manned by motivated soldiers, and lead by men with relevant experience, reinforced and supported from the sea, could accomplish just that thing.

Now, even though I think what I said is enough, I will touch on the open topic of recorded instances where Portuguese attacked much numerically superior forces and prevailed. Most historians, and my humble self, will usually retreat to the position of Portuguese utilizing their experience in amphibious warfare to their advantage. Some will add the better "technological" weapons, and praise the Portuguese firearms, small and large cannon, grenades etc, maybe even add to this list plate armor, crossbows, swords and skills in them, which were beneficial in confined spaces. I would give this line of reasoning some merit but also I would urge caution on taking it to far. Portuguese themselves often praised their enemy weapons and technologies, and while reading Portuguese accounts you won't see them noticing any advantage or disadvantage in weaponry (except maybe in artillery, which was generally admitted by both sides Portuguese had better).
The same Portuguese accounts on the other hand usually praise the Portuguese bravery and valor, while at the same time describing enemy as cowardly and quick to run away. This is no doubt in part self-praising propagandist narrative, but on the other hand such narratives repeat so often, with the results corresponding, that many modern writers accept the possibility that the Portuguese indeed were unusually aggressive, bellicose, highly motivated and overall ferocious fighters in comparison to their adversaries, which lead them to their success in many against the odds situations. I would reserve my judgment on this, but I think it bears mentioning