I was reading a thread the other day about the spanish destruction of Tenochtitlán. A few of the comments suggested that rather than the spanish coming to outright dominate the people of Mexico quickly, that rather their control was tenuous at best. Although they liked to paint a picture of loyal christian subjects under firm control of the crown the reality was much closer to the people of Mexico still holding control and working more with the spanish than as subjugated people. I would take this to mean that it would still be centuries before Mexico was firmly under spanish control and that it would paint a picture of more gradual assimilation than domination.
Hey,
I was one of the people commenting in the thread you mention. Since I've written a bit on this large topic on here, I hope it's ok if I link you to some previous answers of mine about it:
Here I discuss Spanish control over colonial Mexico and resistance to it
I wrote about Spanish influence on indigenous groups in central Mexico before, e.g. in some detail over here (also quite long, with follow ups) .
There are also some of my other answers on related topic over in my AH profile, in case you'd like to have a look.
Very broadly, I'd say that in colonial Mexico (like in other parts of Spanish America) the Spanish had relative secure control over some central areas - esp. the colonial centres central Mexico and parts of Peru, where they could build on the structures of the Aztecs and Incas. But moving further out from those, their power was gradually less strong. So that in more peripheral areas like e.g. Northern New Spain or large parts of the Amazon, during most of the colonial period there was little to no Spanish control.
Also you're right about Spanish influence gradually spreading out - although "assimiliation" is maybe not the best word. I'd rather say long term processes, through which elements of indigenous cultures persist until today, often adapting from Spanish customs along the way. I try to describe some of those processes in those answers.
Hope this helps!