Banks are obliged to check residency when opening account and then send CRS data based on the data you can provide. So for example I have a permanent NIE in spain, when I opened a bank︀ account there, if I showed them the NIE they would send data to the Hacienda︁ ( spain tax authoirty ) if I showed them my passport they would send it︂ to my home country, with my passport and a utility bill from Dubai, they would︃ send CRS messages in Dubai.
Or if you open an account as a foreigner in︄ Dubai, they will send CRS messages based on your passport or on your residency documents.︅ If you later become a UAE resident, they will not send any CRS message as︆ location will be updated. ( mistakes have happened when this update was not done and︇ thus CRS messages where sent anyway, so avoid doing those things and wait for papers︈ ).
If you lose residency status, bank will discover at some point, either by a︉ state message or by a KYC inquiry, and will start sending CRS messages based on︊ proof of residence you provide or your home country. CRS messages are sent once a︋ year if I'm correct.
Dubai having no taxes on individuals means that the tax authority︌ doesn't care if you have accounts in your name, so any CRS message sent to︍ Dubai tax authority is not relevant.