The market cap is the number of share multiplied by the current share price. So this is a made up number because the reality is that not all these share would sell at the current share value.

Essentially, Apple Market Cap raised because people bought shares at a higher price after the announcements.

Well yes and no. Market cap is the total value of all shares for the particular stock combined (not including those held by the company itself). The value of each individual share is determined on the market. No-one directly "owns" this value, since the whole point of stocks is to distribute ownership, so no-one including Apple as an entity "owns" their market cap entirely. If that were the case, there would be no trading, and ergo no value to the shares, and the entire idea of a market cap no longer applies.

Individually though, the value of shares is of course very real. If you own shares and the stock is liquid (as in: there are people willing to buy), you can sell those shares for real money whenever you wish, at the current market price. Unless you want to sell a substantial amount, in which case you may run into trouble finding buyers and / or create significant downward pressure on the price.