There are at least two things being mixed under the term "propagation" here.
One is various caches of local resolvers and recursing name servers remembering information for a set amount of time before they go out and ask an authoritative server again. This has no relevance to your question, but it is what many of those articles you read were talking about.
The other is data moving from a master name server to its secondary name servers. This is relevant to your question. A master name server is where data gets injected into DNS from outside, so that's where your new records begin their lives. Secondary servers check with the master server for new data when they think enough time has passed or when they get prodded to do so (usually, the master server is set to prod them when its information is updated). The way they tell if they need to re-fetch a zone from the master or not is by comparing the serial number in the zone's SOA record between what they have stored locally and what the server has. If the number at the master is higher, the secondary will fetch the whole zone again (usually, other options exist). If the number at the master is not higher, the secondary will assume the information it has is up to date, and do nothing.
The most common reason, by far, for new records not propagating to secondaries is that whoever added the new records forgot to increase the serial number in the SOA record.
