The NI payments are the UK funding for th NHS, in theory, and if the husband had fully paid up his wife would automatically be covered as well.
No it didn't. It used to be that anybody who was lawfully residing in the UK (not illegal or a visitor) could use the NHS bill free as they were ordinarily resident. Some British citizens (UK state pensioners?) living in certain countires, in certain conditions, could also visit the UK for bill free NHS.
The Immigration Act 2014 changed the defination of ordinarily resident to, those who have a valid ILR or British citizenship and who are living in the UK. Brits living abroad can now be billed and some residents in the UK are now billed too, with 50% added to the bill if they don't have insurance to pay.
Your wife on a spouse visa, could use the NHS bill free if she had a valid UK visa, but she would only get that Limited Leave to Remain visa from 6 April 2015, if she paid the IHS.
If she has broken her 5 year route to ILR, then it looks like her 5 years to ILR starts again with her new visa in 2018. If she has overstayed, it will likely affect British citizenship.
Can you give the dates of her immigration and the start and end dates of those visas.