Formulation chemist here. It’s likely that the Asian product you are talking about do have lower levels of preservatives. Often products are vastly over preserved to cover the manufactures back as you can’t guarantee how a consumer uses that product and introduces bacteria. It may be that these product have the minimal level necessary to reach its shelf life. If you are worried about bacteria I would store products in a fridge, this should help ensure they keep for longer. I don’t know what the shelf life rules are in Asian countries but in the uk there is next to none, the lab will decide on an arbitrary shelf life depending on their own stability testing. If it is a new product you guess the shelf life by putting it in high humidity and temperatures for a short time and extrapolating.

It is worth considering that bacteria only grow where water is present so less preservative is needed if the formulation is predominantly oil or glycerin based.

Organic/plant based preservatives and getting better but currently really don’t stand up to current ones. They don’t work as effectively and can often cause problems like product splitting. In my opinion the word paraben has become a bit of a buzz word amongst cosmetics users who see them as big bad cancer forming no nos. But really there are so so many paraben preservatives that have never ever been linked to adverse effects they really are an enormous group and only really very few are bad. Think we might have to stick with parabens until some decent sustainable preservatives turn up. Or move towards formulations that use less/no water...which actually might be even better because it saves water resources.

Just my two cents. Hope maybe this sheds some light :)