I have heard it said (sorry, no refs for you) that when a colony is formed from a parent population, then the colonists 'freeze' in time with respect to language and accents, perhaps cultural aspects and values, and so on. An example is Australia - apparently the Australian accent is similar to a 'British' accent from some time near the early days of the colony (I know that there's no British accent; obviously there would be the influence of many: Irish especially). The parent (UK) changes and evolves, while the smaller colony does so at a much reduced rate.
This might be a better question for the Linguistics Stack Exchange site, but I'll give it a shot. Language divergence or linguistic divergence is "when a language breaks into dialects due to a lack of spatial interaction among speakers of a language, and continued isolation causes new languages to be formed."
The branch of linguistics that deals with this is called dialectology:
Dialectology treats such topics as divergence of two local dialects from a common ancestor and synchronic variation.
Dialectologists are concerned with grammatical features that correspond to regional areas. Thus, they are usually dealing with populations living in specific locales for generations without moving, but also with immigrant groups bringing their languages to new settlements.
There is also the term dialect continuum -- "a range of dialects spoken across some geographical area that differ only slightly between neighboring areas, but as one travels in any direction, these differences accumulate such that speakers from opposite ends of the continuum are no longer mutually intelligible."
The linguists use the term
for the phenomenon of where a language preserves older features, rather than creating new ones (as is often the case).
But it is not a universal that the colonies are more conservative then the home culture. Italian is the most conservative in Romance, and it is the geographically divergent members ones that have the most changes (French and Romanian).
As to English, RP is non-rhotic which is supposedly a newer innovtion. But in America... mostly rhotic but some Southern accents are non-rhotic, mostly corresponding historically to West country accents. So out of all that, how can you really say which one is being conservative and which not?
There are a number of factors connected to how a language dialect(s) develop in a colony. Firstly, the influence of the first colonisers -their original regional dialect in the 'mother country'. Secondly, any contact with and borrowing from other languages -so-called stratum effect, with non-dominant languages being termed substrates (in the US: native languages, German, Dutch, French, etc). Finally, any novel terms, expressions or ideas born out of that contact, not to mention mixing of English dialects from new arrivals -both first and second language English speakers.
In light of the above, the statement that US English is somehow a form of older 'original' English is not easy to support, as there is space for considerable subsequent influence.