What happens to A and B?
Nothing will happen to A. TIPS rates are not based on short-term interest rates that the government sets, but a lookback of the CPI, so the principal and interest will not change the day after a change in rates by the Fed.
For B it's not as clear. Certainly if the Fed raises its rates, the market will act accordingly and may raise its projection of longer-term rates, and that change may have an impact on inflation projections, which may increase the value of a TIPS ETF, or the ETF may go down since the bonds within it have a lower yield than the new market projection of interest rates.
Note that if a hypothetical ETF tracks one specific TIPS bond, as you mention in your comment, then nothing would happen to B either, as a TIPS with one day to maturity will be unaffected by interest rate changes.
In conclusion, is it correct to say that one of the main differences between buying securities in primary and secondary markets is that, in the first case, your security matures and so the risk is low, but in the second case you are subject to market fluctuation and so your risk is way higher?
There is a difference between holding fixed-income funds and holding individual bonds (I would not classify it as "primary" and "secondary" in this case, but buying ETFs versus individual bonds).
Individual bonds have fixed coupons and redemption (or in the TIPS case, a redemption value that is roughly adjusted for inflation). You get the same value back regardless of what happens to interest rates in general.
Bond ETFs, by contrast, do not have guaranteed income. Since the fund contains lots of bonds that go up and down in value, and must buy bonds to replace those that mature or are sold, they are much more sensitive to change in interest rates. There is no "maturity" for ETFs, so you get whatever the value of those funds is when you sell your holdings. It's more a bet on the future on interest rates, with some income in the form of distributions, which may go up and down as well.
Individual bonds also go up and down in value, but if you hold the bond to maturity that change is never materialized. It is just an opportunity cost, since if rates go up, you are earning a lower interest rate than the market rates. You could replace the bond with one of a higher yield, but you will get less than face value when you sell the bond.
So it's not as simple as that funds and ETFs are "more risky" - they have similar risks, but the material effect of those risks is different.