I have spent some time in Kenya and I have heard hardly anyone using the numbers in accordance with the nouns. People would for example say: "Walimu mbili". Is that common colloquial use in Tanzania as well? Or is this something specific to Kenya? Would most people in Tanzania (or coastal areas of Kenya) understand me if I say "Walimu mbili", or think that this is a bit weird?
Swahili is used at the native language of some people, primarily on the Zanzibar islands and adjacent coastal areas, and as a lingua franca throughout the rest of its range.
Lingua francas usually end up being simplified and regularised a lot by being spoken by people who have learned it imperfectly as a second language. I'm guessing that's part of the reason why Swahili is, from what I've seen, simpler in grammar and pronunciation than its neighbouring Bantu relatives, with five vowels instead of seven, no tones and, if you look at the grammar of some other Bantu languages, you'll appreciate how simple Swahili really is.
As a lingua franca, it is acquiring new cohorts of native speakers, especially in urban areas where, where couples with different native languages who communicate with each other in Swahili have children. I wouldn't be surprised if the grammar is further simplified/modified in urban areas outside of its original range of native speakers.
One big simplification that I know of is that a lot of speakers use agreement markers only depending on animacy, with adjectives, verbs, possessives etc. agreeing with nouns not based on their class but based on their animacy, with animate nouns taking agreements in the 1/2 class (M-WA) (true also in standard Swahili) and inanimate nouns taking agreements in the 9/10 class (N-N). For example, in this way of speaking Swahili, people would not say the standard Kitanda changu ni kizuri. (My bed is good.) but Kitanda yangu ni nzuri.
In any case, this course is teaching us the standard Swahili, which is good because it's fairly complex compared to how it's often used as a lingua franca. It's good to learn the most complex, standard form because you can always simplify it if you like, but if you learn the simplified form, it's harder to learn the rules for the more complicated standard.