Yes, they are supposed to take out the tax - only a portion of the National Insurance and income tax you pay goes towards healthcare, so the rest of the NI is for income-related benefits - maternity pay, job seekers allowances, things like that.
The £600 you paid with the visa has nothing to do with paying National Insurance or taxes. It's called the Immigration Health Surcharge (IHS). It is not an insurance of any kind, it's a mandatory contribution to your NHS healthcare costs in the UK and it allows you to get all your healthcare free at point of service... You can't get any of it back. Annoyingly though it basically means you pay twice for healthcare - once out of your income and once with the IHS. It's unfortunately the nature of living in the UK on a visa in 2016.
I don't know why you paid £690 instead of £600 though because it's a fixed amount - £200 per year of the visa, rounded up to full years if it covers more than 6 months of a year, so a 33-month spousal visa has a £600 charge, while a 30-month extension has a £500 charge.
The only reason I can think why you might have paid £690 is because I think it's charged in US dollars and the exchange rate set by UKVI at that time might have meant you paid a bit more. If that's the case, then you can't get the £90 back either because that's how much the surcharge was when you applied.
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