Does Stellaris end at a certain time

I took a look at the Wikipedia and based on my understanding it works like this:

Ethics divergence effects how likely the pop is going to follow the governing ethics. If a population has -20% Ethics Diversion (like the conformist trait) the more likely they are to switch the the governing ethics. A population with say +20% ethics divergence are more likely to adopt different ethics and start factions etc.

Today's @StellarisGame fact: Negative ethics divergence will make pops drift towards your empire ethos.

In your case, if you make their ethics divergence negative, it will increase the chances that they will adopt your ethics and vice versa if it is positive, they are more likely to adopt new ethics or maintain ones that are not your own. A good thing to note, if the stat is green it is usually better for you so look at the color of the percentage (if it has a color).

EDIT
Missed out some sources for evidence that the above is true. Wiki page doesn't actually say that negative ethics divergence increase chance of pops adopting ethics of governing bodies. Following links provide evidence by Project Lead, Martin Anward. I highly recommend checking out the twitter link, has loads of useful facts.
Martin Anward's twitter fact
Reddit Source

You can check the modifiers by hovering over the red x (or the green checkmark) next to the demand vassalization text. It's a detailed breakdown of which factors speak for and against accepting the demand. If the total number is positive, you'll see a green checkmark and they'll accept the demand, otherwise they won't.

Here are the most important factors:

1. Ethics. Similar ethics provide boosts to this, very important, some ethics like fanatical xenophobe will prevent a peaceful vassalization entirely. You cannot influence this.

2. Empire strength, being stronger, i.e. having the bigger fleet and bigger empire provides significant bonuses

3. Opinion, the biggest factor is opinion there are several ways to increase it: mutual rivals, embassy, treaties (border access, non-aggression, guaranteeing, research agreement), making the empire like you is the most important aspect of peaceful vassalization. Keep in mind, you CANNOT engage into an alliance with them, as an alliance locks you in as equal partners and disables vassalization.

It is generally pretty hard to get a purely peaceful vassalization, especially if your ethics diverge somewhat.

There is a form of military/peaceful vassalization though, that goes beyond forcing an enemy to submit. If in a war, you choose to liberate enemy planets instead of conquering them, this will create a new empire with your government ethics, on top of that, you get a massive +100 opinion for being their liberator. This usually makes peaceful vassalization of the liberated empire very easy.